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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:35:29 +0000Fault-tolerant cluster of networking elements
https://resolver.caltech.edu/CaltechETD:etd-08152001-144501
Authors: {'items': [{'email': 'fan@rainfinity.com', 'id': 'Fan-C-C', 'name': {'family': 'Fan', 'given': 'Chenggong Charles'}, 'show_email': 'YES'}]}
Year: 2001
DOI: 10.7907/R15B-VD58
The explosive growth of the Internet demands higher reliability and performance than what the current networking infrastructure can provide. This dissertation explores novel architectures and protocols that provide a methodology for grouping together multiple networking elements, such as routers, gateways, and switches, to create a more reliable and performant distributed networking system. Clustering of networking elements is a novel concept that requires the invention of distributed computing protocols that facilitate efficient and robust support of networking protocols. We introduce the Raincore protocol architecture that achieves these goals by bridging the fields of computer networks and distributed systems.
In designing Raincore, we paid special attention to the unique requirements from the networking environment. First, networking clusters need to scale up the networking throughput in addition to the scaling up of computing power. Second, task switching between the different services supported by a networking element has a major negative impact on performance. Third, fast fail-over time is critical for maintaining network connections in the event of failures. We discuss in depth the design of Raincore Group Communication Manager that addresses the forgoing requirements and provides group membership management and reliable multicast transport. It is based on a novel token-ring protocol. We prove that this protocol is formally correct, namely, it satisfies the set of formal specifications that defines the Group Membership problem.
The creation of Raincore has already made a substantial impact both at Caltech and the academic community as well as in the industry. The first application is SNOW, a scalable web server cluster that is part of RAIN, a collaborative project between Caltech and JPL/NASA. The second application is RainWall, a commercial solution created by Rainfinity, a Caltech spin-off company, that provides the first fault-tolerant and scalable firewall cluster. These applications exhibit the fast fail-over response, low overhead, and near-linear scalability of the Raincore protocols.
In addition, we studied fault-tolerant networking architectures. In particular, we considered efficient constructions of extra-stage fault-tolerant Multistage Interconnection Networks. Multistage Interconnection Networks provide a way to construct a larger switching network using smaller switching elements. We discovered an optimal family of constructions, in the sense that it requires the least number of extra components to tolerate multiple switching element failures. We prove that this is the only family of constructions that has this optimal fault-tolerance property.
https://thesis.library.caltech.edu/id/eprint/3121Periodic Broadcast Scheduling for Data Distribution
https://resolver.caltech.edu/CaltechETD:etd-05132005-151145
Authors: {'items': [{'id': 'Foltz-Kevin-E', 'name': {'family': 'Foltz', 'given': 'Kevin E.'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/980Q-RQ20
As wireless computer networks grow in size and complexity, we are faced with the problem of providing scalable, high-bandwidth service to their users. Wired networks typically use "data pull," where users send requests to a server and the server responds with the desired information. In the wireless domain, "data push" promises to provide better performance for many applications [1]. The broadcast domain that is typical of wireless communication is very effective in distributing information to large audiences.
The idea of broadcast disks has been around since the Teletext system [3]. There is now an interest in applying these ideas to wireless computer networks. There are some interesting research questions about scheduling for data distribution. Computing optimal schedules has been shown to be difficult [18]. The optimal schedules themselves, however, seem to be less complex, and often periodic [4]. Xu [24] looks at the scheduling of streaming data, which involves splitting the data into smaller pieces. The idea of error correction is also important for wireless transmission due to the noisy nature of the channel [6].
We look at scheduling data for broadcast. We compare time-division scheduling and frequency-division scheduling for data items of equal length. We show that time-division is better for sending dynamic data. We then find optimal time-division schedules for two items. We show how the freedom to split items into smaller pieces can give improvements in performance. With a single split, where each of two items is split in half, we find the optimal schedules for items of equal length.
We continue with the idea of splitting items, and show what happens when the number of splits is very large. Then, we examine what happens when we add streaming data to our broadcast. We compare time-division and frequency-division as before, and now also look at a mix of the two. We prove bounds on where the mix is the best broadcast method.https://thesis.library.caltech.edu/id/eprint/1777Rate Loss of Network Source Codes
https://resolver.caltech.edu/CaltechETD:etd-05232002-173821
Authors: {'items': [{'id': 'Feng-Hanying', 'name': {'family': 'Feng', 'given': 'Hanying'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/GVDP-7248
In this thesis, I present bounds on the performance of a variety of network source codes. These <em>rate loss</em> bounds compare the rates achievable by each network code to the rate-distortion bound <em>R(D)</em> at the corresponding distortions. The result is a collection of optimal performance bounds that are easy to calculate.
I first present new bounds for the rate loss of multi-resolution source codes (MRSCs). Considering an <em>M</em>-resolution code with <em>M</em>>=2, the rate loss at the <em>i</em>th resolution with distortion <em>D_i</em> is defined as <em>L_i=R_i-R(D_i)</em>, where <em>R_i</em> is the rate achievable by the MRSC at stage <em>i</em>. For 2-resolution codes, there are three scenarios of particular interest: (i) when both resolutions are equally important; (ii) when the rate loss at the first resolution is 0 (<em>L_1=0</em>); (iii) when the rate loss at the second resolution is 0 (<em>L_2=0</em>). The work of Lastras and Berger gives constant upper bounds for the rate loss in scenarios (i) and (ii) and an asymptotic bound for scenario (iii). In this thesis, I show a constant bound for scenario (iii), tighten the bounds for scenario (i) and (ii), and generalize the bound for scenario (ii) to <em>M</em>-resolution greedy codes.
I also present upper bounds for the rate losses of additive MRSCs (AMRSCs), a special MRSC. I obtain two bounds on the rate loss of AMRSCs: one primarily good for low rate coding and another which depends on the source entropy.
I then generalize the rate loss definition and present upper bounds for the rate losses of multiple description source codes. I divide the distortion region into three sub-regions and bound the rate losses by small constants in two sub-regions and by the joint rate losses of a normal source with the same variance in the other sub-region.
Finally, I present bounds for the rate loss of multiple access source codes (MASCs). I show that lossy MASCs can be almost as good as codes based on joint source encoding.https://thesis.library.caltech.edu/id/eprint/1965Controlled Lagrangian and Hamiltonian Systems
https://resolver.caltech.edu/CaltechTHESIS:10112010-161816245
Authors: {'items': [{'id': 'Chang-Dong-Eui', 'name': {'family': 'Chang', 'given': 'Dong Eui'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/3DRR-ZV53
<p>any control systems are mechanical systems. The unique feature of mechanical systems is the notion of energy, which gives much information on the stability of equilibria. Two kinds of forces are associated with the energy: dissipative force and gyroscopic force. A dissipative force is, by definition, a force which decreases the energy, and a gyroscopic force is, by definition, a force that does not change the energy. Gyroscopic forces add couplings to the dynamics. In this thesis, we develop a control design methodology which makes full use of these three physical notions: energy, dissipation, and coupling.</p>
<p>First, we develop the method of controlled Lagrangian systems. It is a systematic procedure for designing stabilizing controllers for mechanical systems by making use of energy, dissipative forces, and gyroscopic forces. The basic idea is as follows: Suppose that we are given a mechanical system and want to design a controller to asymptotically stabilize an equilibrium of interest. We look for a feedback control law such that the closed-loop dynamics can be also described by a new Lagrangian with a dissipative force and a gyroscopic force where the energy of the new Lagrangian has a minimum at the equilibrium. Then we check for asymptotic stability by applying the Lyapunov stability theory with the new energy as a Lyapunov function.</p>
<p>Next, we show that the method of controlled Lagrangian systems and its Hamiltonian counterpart, the method of controlled Hamiltonian systems, are equivalent for simple mechanical systems where the underlying Lagrangian is of the form kinetic minus potential energy. In addition, we extend both the Lagrangian and Hamiltonian sides of this theory to include systems with symmetry and discuss the relevant reduction theory.</p>https://thesis.library.caltech.edu/id/eprint/6128Network Source Coding: Theory and Code Design for Broadcast and Multiple Access Networks
https://resolver.caltech.edu/CaltechETD:etd-05302003-125004
Authors: {'items': [{'id': 'Zhao-Qian', 'name': {'family': 'Zhao', 'given': 'Qian'}, 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/61XN-MV62
<p>In the information age, network systems and applications have been growing rapidly to provide us with more versatile and high bit rate services. However, the limited bandwidth restricts the amount of information that can be sent through the networks. Thus efficient data representation or source coding is imperative for future network development. Distinct from the traditional source coding strategy, network source codes take advantage of the network topology and are able to maximally compress data before transmission.</p>
<p>In this thesis, I present a variety of source coding techniques for use in network environments and demonstrate the benefits of network source codes over traditional source codes from both theoretical and practical perspectives.</p>
<p>First, I address source coding for broadcast systems. The results I obtain include derivation of the theoretical limits of broadcast system source codes, algorithm design for optimal broadcast system vector quantizers, implementation of the optimal code, and experimental results.</p>
<p>Then, I focus on multiple access systems which are the dual systems of broadcast systems. I present the properties of multiple access source codes and generalize traditional entropy code design algorithms to attain the corresponding optimal multiple access source codes for arbitrary joint source statistics. I further introduce a family of polynomial complexity code design algorithms that approximates the optimal solutions. Application to universal coding for multiple access networks when the joint source statistics are unknown a priori is briefly discussed. Finally, I demonstrate algorithmic performance by showing experimental results on a variety of data sets.</p>
<p>inally, in seeking a simple lossy source coding method for general networks, I apply entropy constrained dithered quantization in network source code design and present the coding results for multi-resolution source codes and multiple access source codes. Multi-resolution and multiple access dithered quantizers are low complexity codes that achieve performance very close to the theoretical rate-distortion bound.</p>https://thesis.library.caltech.edu/id/eprint/2289Data Collection and Distribution in Sensory Networks
https://resolver.caltech.edu/CaltechETD:etd-05312004-205111
Authors: {'items': [{'id': 'Florens-Cédric-Jean-Paul', 'name': {'family': 'Florens', 'given': 'Cédric Jean Paul'}, 'show_email': 'NO'}]}
Year: 2004
DOI: 10.7907/ZK3J-VB92
<p>The deployment of large-scale, low-cost, low-power, multifunctional sensory networks brings forward numerous and diverse research challenges. Critical to the design of systems that must operate under extreme resource constraints, the understanding of the fundamental performance limits of sensory networks is a research topic of particular importance. This thesis examines, in this respect, an essential function of sensory networks, viz., data collection, that is, the aggregation at the user location of information gathered by sensor nodes.</p>
<p>In the first part of this dissertation we study, via simple discrete mathematical models, the time performance of the data collection and data distribution tasks in sensory networks. Specifically, we derive the minimum delay in collecting sensor data for networks of various topologies such as line, multi-line, tree and give corresponding optimal scheduling strategies assuming that the amount of data observed at each node is finite and known at the beginning of the data collection phase. Furthermore, we bound the data collection time on general graph networks.</p>
<p>In the second part of this dissertation we take the view that the amount of data collected at a node is random and study the statistics of the data collection time. Specifically, we analyze the average minimum delay in collecting randomly located/distributed sensor data for networks of various topologies when the number of nodes becomes large. Furthermore, we analyze the impact of various parameters such as lack of synchronization, size of packet, transmission range, and channel packet erasure probability on the optimal time performance. Our analysis applies to directional antenna systems as well as omnidirectional ones. We conclude our study with a simple comparative analysis showing the respective advantages of the two systems.</p>
https://thesis.library.caltech.edu/id/eprint/2325On Source Coding for Networks
https://resolver.caltech.edu/CaltechETD:etd-05282004-170744
Authors: {'items': [{'id': 'Fleming-Michael-Ian-James', 'name': {'family': 'Fleming', 'given': 'Michael Ian James'}, 'show_email': 'NO'}]}
Year: 2004
DOI: 10.7907/CY48-QJ71
<p>In this thesis, I examine both applied and theoretical issues in network source coding.</p>
<p>The applied results focus on the construction of locally rate-distortion-optimal vector quantizers for networks. I extend an existing vector quantizer design algorithm for arbitrary network topologies [1] to allow for the use of side information at the decoder and for the presence of channel errors. I show how to implement the algorithm and use it to design codes for several different systems. The implementation treats both fixed-rate and variable-rate quantizer design and includes a discussion of convergence and complexity. Experimental results for several different systems demonstrate in practice some of the potential performance benefits (in terms of rate, distortion, and functionality) of incorporating a network's topology into the design of its data compression system.</p>
<p>The theoretical work covers several topics. Firstly, for a system with some side information known at both the encoder and the decoder, and some known only at the decoder, I derive the rate-distortion function and evaluate it for binary symmetric and Gaussian sources. I then apply the results for binary sources in evaluating the binary symmetric rate-distortion function for a system where the presence of side information at the decoder is unreliable. Previously, only upper and lower bounds were known for that problem. Secondly, I address with an example the question of whether feedback from a decoder to an encoder ever enlarges the achievable rate region for lossless network source coding of memoryless sources. Thirdly, I show how cutset methods can yield quick and simple rate-distortion converses for any source coding network. Finally, I present rate-distortion results for two different broadcast source coding systems.</p>https://thesis.library.caltech.edu/id/eprint/2199Optimized Network Data Storage and Topology Control
https://resolver.caltech.edu/CaltechETD:etd-05272004-163315
Authors: {'items': [{'email': 'ajiang@cse.tamu.edu', 'id': 'Jiang-Anxiao-Andrew', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}, 'orcid': '0000-0002-0120-7930', 'show_email': 'YES'}]}
Year: 2004
DOI: 10.7907/91R7-MH71
<p>This thesis addresses two key challenges for network data-storage systems: optimizing data placement for highly efficient and robust data access, and constructing network topologies that facilitate data transmission scalable to both network sizes and network dynamics. It focuses on two new topics — data placement using erasure-correcting codes, and topology control for nodes in normed spaces. The first topic generalizes traditional file-assignment problems, and has the distinct feature of interleavingly placing data in networks. The second topic emphasizes the construction of network topologies that achieve excellent global performance in comprehensive measurements, through purely local decisions on connectivity. The results of the thesis deepen the current understanding on these important and intriguing topics, and follow a mathematically rigorous approach.</p>
https://thesis.library.caltech.edu/id/eprint/2137Space-Time Code Design and Its Applications in Wireless Networks
https://resolver.caltech.edu/CaltechETD:etd-09072004-204814
Authors: {'items': [{'email': 'yindi@ualberta.ca', 'id': 'Jing-Yindi', 'name': {'family': 'Jing', 'given': 'Yindi'}, 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/QYN9-0Z55
<p>This thesis has two main contributions: the designs of differential/non-differential unitary space-time codes for multiple-antenna systems and the analysis of the diversity gain when using space-time coding among nodes in wireless networks.</p>
<p>Capacity has long been a bottleneck in wireless communications. Recently, multiple-antenna techniques have been used in wireless communications to combat the fading effect, which improves both the channel capacity and performance greatly. A recently proposed method for communicating with multiple antennas over block-fading channels is unitary space-time modulation, which can achieve the channel capacity at high SNR. However, it is not clear how to generate well performing unitary space-time codes that lend themselves to efficient encoding and decoding. In this thesis, the design of unitary space-time codes using Cayley transform is proposed. The codes are designed based on an information-theoretic criterion and have a polynomial-time near-maximum-likelihood decoding algorithm. Simulations suggest that the resulting codes allow for effective high-rate data transmissions in multiple-antenna communication systems without knowing the channel. Another well-known transmission scheme for multiple-antenna systems with unknown channel information at both the transmitter and the receiver is differential unitary space-time modulation. It can be regarded as a generalization of DPSK and is suitable for continuous fading. In differential unitary space-time modulation, fully diverse constellations, i.e., sets of unitary matrices whose pairwise differences are non-singular, are wanted for their good pairwise error properties. In this thesis, Lie groups and their representations are used in solving the design problem. Fully diverse differential unitary space-time codes for systems with four and three transmit antennas are constructed based on the Lie groups Sp(2) and SU(3). The designed codes have high diversity products, lend themselves to a fast maximum-likelihood decoding algorithm, and simulation results show that they outperform other existing codes, especially at high SNR.</p>
<p>Then the idea of space-time coding devised for multiple-antenna systems is applied to communications over wireless networks. In wireless relay networks, the relay nodes encode the signals they receive from the transmit node into a distributed space-time code and transmit the encoded signals to the receive node. It is shown in this thesis that at very high SNR, the diversity gain achieved by this scheme is almost the same as that of a multiple-antenna system whose number of transmit antennas is the same as the number of relay nodes in the network, which means that the relay nodes work as if they can cooperate fully and have full knowledge of the message. However, at moderate SNR, the diversity gain of the wireless network is inferior to that of the multiple-antenna system. It is further shown that for a fixed total power consumed in the network, the optimal power allocation is that the transmitter uses half the power and the relays share the other half fairly. This result addresses the question of what performance a relay network can achieve. Both it and its extensions have many applications to wireless ad hoc and sensory network communications.</p>https://thesis.library.caltech.edu/id/eprint/3369Interval Modulation: A New Paradigm for the Design of High Speed Communication Systems
https://resolver.caltech.edu/CaltechETD:etd-07072004-154316
Authors: {'items': [{'email': 'saleem@paradise.caltech.edu', 'id': 'Mukhtar-Saleem', 'name': {'family': 'Mukhtar', 'given': 'Saleem'}, 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/6F03-MP11
In this thesis we propose a new, biologically inspired, paradigm for the design of high speed communication systems. The paradigm consists of a new modulation format referred to as Interval Modulation (IM). In order to transmit data in an efficient manner using this format, new coding techniques are needed. In this thesis we propose a coding technique based on variable length to variable length prefix trees and code construction algorithms are outlined. These codes are referred to as Interval Modulation Codes (IMC). Furthermore, data encoded with this modulation format cannot be transmitted or received using conventional synchronous CDR based receivers. In this thesis we outline a new asynchronous circuit architecture for both the transmitter and receiver. The architecture is based on active delay lines and eliminates the need for clock recovery.https://thesis.library.caltech.edu/id/eprint/2818Scalable Analysis of Nonlinear Systems Using Convex Optimization
https://resolver.caltech.edu/CaltechETD:etd-05082005-100243
Authors: {'items': [{'email': 'antonis@eng.ox.ac.uk', 'id': 'Papachristodoulou-Antonis', 'name': {'family': 'Papachristodoulou', 'given': 'Antonis'}, 'orcid': '0000-0002-3565-8967', 'show_email': 'YES'}]}
Year: 2005
DOI: 10.7907/5YG6-JG32
<p>In this thesis, we investigate how convex optimization can be used to analyze different classes of nonlinear systems at various scales algorithmically. The methodology is based on the construction of appropriate Lyapunov-type certificates using sum of squares techniques.</p>
<p>After a brief introduction on the mathematical tools that we will be using, we turn our attention to robust stability and performance analysis of systems described by Ordinary Differential Equations. A general framework for constrained systems analysis is developed, under which stability of systems with polynomial, non polynomial vector fields and switching systems, as well as estimating the region of attraction and the L<sub>2</sub> gain can be treated in a unified manner. Examples from biology and aerospace illustrate our methodology.</p>
<p>We then consider systems described by Functional Differential Equations (FDEs), i.e., time-delay systems. Their main characteristic is that they are infinite dimensional, which complicates their analysis. We first show how the complete Lyapunov-Krasovskii functional can be constructed algorithmically for linear time delay systems. Then, we concentrate on delay-independent and delay-dependent stability analysis of nonlinear FDEs using sum of squares techniques. An example from ecology is given.</p>
<p>The scalable stability analysis of congestion control algorithms for the Internet is investigated next. The models we use result in an arbitrary interconnection of FDE subsystems, for which we require that stability holds for arbitrary delays, network topologies and link capacities. Through a constructive proof, we develop a Lyapunov functional for FAST - a recently developed network congestion control scheme - so that the Lyapunov stability properties scale with the system size. We also show how other network congestion control schemes can be analyzed in the same way.</p>
<p>Finally, we concentrate on systems described by Partial Differential Equations. We show that axially constant perturbations of the Navier-Stokes equations for Hagen-Poiseuille flow are globally stable, even though the background noise is amplified as R<sup>3</sup> where R is the Reynolds number, giving a 'robust yet fragile' interpretation. We also propose a sum of squares methodology for the analysis of systems described by parabolic PDEs.</p>
<p>We conclude this work with an account for future research.</p>https://thesis.library.caltech.edu/id/eprint/1678Heterogeneous Congestion Control Protocols
https://resolver.caltech.edu/CaltechETD:etd-05242006-170918
Authors: {'items': [{'email': 'atang@ece.cornell.edu', 'id': 'Tang-Ao-Kevin', 'name': {'family': 'Tang', 'given': 'Ao (Kevin)'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/eh43-pa83
<p>Homogeneity of price is an implicit yet fundamental assumption underlying price based resource allocation theory. In this thesis, we study the effects of relaxing this assumption by examining a concrete engineering system (network with heterogeneous congestion control protocols). The behavior of the system turns out to be very different from the homogeneous case and can potentially be much more complicated. A systematic theory is developed that includes all major properties of equilibrium of the system such as existence, uniqueness, optimality, and stability. In addition to analysis, we also present numerical examples, simulations, and experiments to illustrate the theory and verify its predictions.</p>
<p>When heterogeneous congestion control protocols that react to different pricing signals share the same network, the resulting equilibrium can no longer be interpreted as a solution to the standard utility maximization problem as the current theory suggests. After introducing a mathematical formulation of network equilibrium for multi-protocol networks, we prove the existence of equilibrium under mild assumptions. For almost all networks, the equilibria are locally unique. They are finite and odd in number. They cannot all be locally stable unless the equilibrium is globally unique. We also derive two conditions for global uniqueness. By identifying an optimization problem associated with every equilibrium, we show that every equilibrium is Pareto efficient and provide an upper bound on efficiency loss due to pricing heterogeneity. Both intra-protocol and inter-protocol fairness are then discussed. On dynamics, various stability results are provided. In particular it is shown that if the degree of pricing heterogeneity is small enough, the network equilibrium is not only unique but also locally stable. Finally, a distributed algorithm is proposed to steer a network to the unique equilibrium that maximizes the aggregate utility, by only updating a linear parameter in the sources' algorithms in a slow timescale.</p>https://thesis.library.caltech.edu/id/eprint/2011Distributed Gradient Systems and Dynamic Coordination
https://resolver.caltech.edu/CaltechETD:etd-06262006-171822
Authors: {'items': [{'id': 'Spanos-Demetri-Polychronis', 'name': {'family': 'Spanos', 'given': 'Demetri Polychronis'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/D1NJ-KF96
<p>Many systems comprised of interconnected sub-units exhibit coordinated behaviors; social groups, networked computers, financial markets, and numerous biological systems come to mind. There has been long-standing interest in developing a scientific understanding of coordination, both for explanatory power in the natural and economic sciences, and also for constructive power in engineering and applied sciences. This thesis is an abstract study of coordination, focused on developing a systematic "design theory" for producing interconnected systems with specifiable coordinated behavior; this is in contrast to the bulk of previous work on this subject, in which any design component has been primarily ad-hoc.</p>
<p>The main theoretical contribution of this work is a geometric formalism in which to cast distributed systems. This has numerous advantages and "naturally" parametrizes a wide class of distributed interaction mechanisms in a uniform way. We make use of this framework to present a model for distributed optimization, and we introduce the distributed gradient as a general design tool for synthesizing dynamics for distributed systems. The distributed optimization model is a useful abstraction in its own right and motivates a definition for a distributed extremum. As one might expect, the distributed gradient is zero at a distributed extremum, and the dynamics of a distributed gradient flow must converge to a distributed extremum. This forms the basis for a wide variety of designs, and we are in fact able to recover a widely studied distributed averaging algorithm as a very special case.</p>
<p>We also make use of our geometric model to introduce the notion of coordination capacity; intuitively, this is an upper bound on the "complexity" of coordination that is feasible given a particular distributed interaction structure. This gives intuitive results for local, distributed, and global control architectures, and allows formal statements to be made regarding the possibility of "solving" certain optimization problems under a particular distributed interaction model.</p>
<p>Finally, we present a number of applications to illustrate the theoretical approach presented; these range from "standard" distributed systems tasks (leader election and clock synchronization) to more exotic tasks like graph coloring, distributed account balancing, and distributed statistical computations.</p>https://thesis.library.caltech.edu/id/eprint/2735Distributed Speculations: Providing Fault-Tolerance and Improving Performance
https://resolver.caltech.edu/CaltechETD:etd-06022006-140421
Authors: {'items': [{'id': 'Țăpuș-Cristian', 'name': {'family': 'Țăpuș', 'given': 'Cristian'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/YZCK-4T29
<p>This thesis introduces a new programming model based on speculative execution and it examines the use of speculations, a form of distributed transactions, for improving the performance, reliability and fault tolerance of distributed systems. A speculation is defined as a computation that is based on an assumption that is not validated before the computation is started. If the assumption is later invalidated the computation is aborted and the state of the program is rolled back; if the assumption is validated, the results of the computation are committed. The primary difference between a speculation and a transaction is that a speculation is not isolated---for example, a speculative computation may send and receive messages, and it may modify shared objects. As a result, processes that share those objects may be absorbed into a speculation.</p>
<p>The contributions presented in this thesis include:
<ul>
<li>the introduction of a new programming model based on speculations,</li>
<li>the definition of new speculative programming language constructs,</li>
<li>the formal specification of the semantics of various speculative execution models, including message passing and shared objects,</li>
<li>the implementation of speculations in the Linux kernel in a transparent manner, and</li>
<li>the design and implementation of components of a distributed filesystem that supports speculations and guarantees sequential consistency of concurrent accesses to files.</li>
</ul></p>https://thesis.library.caltech.edu/id/eprint/2402Data Complexity in Machine Learning and Novel Classification Algorithms
https://resolver.caltech.edu/CaltechETD:etd-04122006-114210
Authors: {'items': [{'id': 'Li-Ling', 'name': {'family': 'Li', 'given': 'Ling'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/EW2G-9986
<p>This thesis summarizes four of my research projects in machine learning. One of them is on a theoretical challenge of defining and exploring complexity measures for data sets; the others are about new and improved classification algorithms.</p>
<p>We first investigate the role of data complexity in the context of binary classification problems. The universal data complexity is defined for a data set as the Kolmogorov complexity of the mapping enforced by that data set. It is closely related to several existing principles used in machine learning such as Occam's razor, the minimum description length, and the Bayesian approach. We demonstrate the application of the data complexity in two learning problems, data decomposition and data pruning. In data decomposition, we illustrate that a data set is best approximated by its principal subsets which are Pareto optimal with respect to the complexity and the set size. In data pruning, we show that outliers usually have high complexity contributions, and propose methods for estimating the complexity contribution. Experiments were carried out with a practical complexity measure on several toy problems.</p>
<p>We then propose a family of novel learning algorithms to directly minimize the 0/1 loss for perceptrons. A perceptron is a linear threshold classifier that separates examples with a hyperplane. Unlike most perceptron learning algorithms, which require smooth cost functions, our algorithms directly minimize the 0/1 loss, and usually achieve the lowest training error compared with other algorithms. The algorithms are also computationally efficient. Such advantages make them favorable for both standalone use and ensemble learning, on problems that are not linearly separable. Experiments show that our algorithms work very well with AdaBoost.</p>
<p>We also study ensemble methods that aggregate many base hypotheses in order to achieve better performance. AdaBoost is one such method for binary classification problems. The superior out-of-sample performance of AdaBoost has been attributed to the fact that it minimizes a cost function based on the margin, in that it can be viewed as a special case of AnyBoost, an abstract gradient descent algorithm. We provide a more sophisticated abstract boosting algorithm, CGBoost, based on conjugate gradient in function space. When the AdaBoost exponential cost function is optimized, CGBoost generally yields much lower cost and training error but higher test error, which implies that the exponential cost is vulnerable to overfitting. With the optimization power of CGBoost, we can adopt more "regularized" cost functions that have better out-of-sample performance but are difficult to optimize. Our experiments demonstrate that CGBoost generally outperforms AnyBoost in cost reduction. With suitable cost functions, CGBoost can have better out-of-sample performance.</p>
<p>A multiclass classification problem can be reduced to a collection of binary problems with the aid of a coding matrix. The quality of the final solution, which is an ensemble of base classifiers learned on the binary problems, is affected by both the performance of the base learner and the error-correcting ability of the coding matrix. A coding matrix with strong error-correcting ability may not be overall optimal if the binary problems are too hard for the base learner. Thus a trade-off between error-correcting and base learning should be sought. In this paper, we propose a new multiclass boosting algorithm that modifies the coding matrix according to the learning ability of the base learner. We show experimentally that our algorithm is very efficient in optimizing the multiclass margin cost, and outperforms existing multiclass algorithms such as AdaBoost.ECC and one-vs-one. The improvement is especially significant when the base learner is not very powerful.</p>https://thesis.library.caltech.edu/id/eprint/1361Broadband Wireless Broadcast Channels: Throughput, Performance, and PAPR Reduction
https://resolver.caltech.edu/CaltechETD:etd-08292005-100440
Authors: {'items': [{'id': 'Sharif-Masoud', 'name': {'family': 'Sharif', 'given': 'Masoud'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/25JK-Z952
<p>The ever-growing demand for higher rates and better quality of service in cellular systems has attracted many researchers to study techniques to boost the capacity and improve the performance of cellular systems. The main candidates to increase the capacity are to use multiple antennas or to increase the bandwidth. This thesis attempts to solve a few challenges regarding scheduling schemes in the downlink of cellular networks, and the implementation of modulation schemes suited for wideband channels.</p>
<p>Downlink scheduling in cellular systems is known to be a bottleneck for future broadband wireless communications. Information theoretic results on broadcast channels provide the limits for the maximum achievable rates for each receiver and transmission schemes to achieve them. It turns out that the sum-rate capacity (sum-rate (or throughput) refers to the sum of the transmission rates to all users) of a multi-antenna broadcast channel heavily depends on the availability of channel state information (CSI) at the transmitter. Unfortunately, the dirty paper coding (DPC) scheme which achieves the capacity region is extremely computationally intensive especially in multiuser context. Furthermore, relying on the assumption that full CSI is available from all the n users may not be feasible in practice.</p>
<p>In the first part of the thesis, we obtain the scaling law of the sum-rate capacity for large n and for a homogeneous fading MIMO (multiple input multiple output) broadcast channel, and then propose a simple scheme that only requires little (partial) CSI and yet achieves the same scaling law. Another important issue in downlink scheduling is to maintain fairness among users with different distances to the transmitter. Interestingly, we prove that our scheduling scheme becomes fair provided that the number of transmit antennas is large enough. We further analyze the impact of using a throughput optimal scheduling on the delay in sending information to the users. Finally, we look into the problem of differentiated rate scheduling in which different users demand for different sets of rates. We obtain explicit scheduling schemes to achieve the rate constraints.</p>
<p>In the second part of the thesis, we focus on orthogonal frequency division multiplexing (OFDM), which is the most promising technique for broadband wireless channels (mainly due to its simplicity of channel equalization even in a severe multipath fading environment). The main disadvantage of this modulation, however, is its high peak to mean envelope power ratio (PMEPR). This is due to the fact that the OFDM signal consists of many (say n) harmonically related subcarriers which may, in the worst-case, add up constructively and lead to large peaks (of order n) in the signal.</p>
<p>Despite this worst-case performance, we show that when each subcarrier is chosen from some given constellation, the PMEPR behaves like log{n} almost surely, for large n. This implies that there exist almost full-rate codes with a PMEPR of log{n} for large n. We further prove that there exist codes with rate not vanishing to zero such that the PMEPR is less than a constant (independent of n). We also construct high rate codes with a guaranteed PMEPR of log{n}. Simulation results show that in a system with 128 subcarriers and using 16QAM, the PMEPR of a multicarrier signal can be reduced from 13.5 to 3.4 which is within 1.6dB of the PMEPR of a single carrier system.</p>https://thesis.library.caltech.edu/id/eprint/3264A Theoretical Study of Internet Congestion Control: Equilibrium and Dynamics
https://resolver.caltech.edu/CaltechETD:etd-11122005-082753
Authors: {'items': [{'id': 'Wang-Jianto', 'name': {'family': 'Wang', 'given': 'Jiantao'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/4DQ0-GA49
<p>In the last several years, significant progress has been made in modelling the Internet congestion control using theories from convex optimization and feedback control. In this dissertation, the equilibrium and dynamics of various congestion control schemes are rigorously studied using these mathematical frameworks.</p>
<p>First, we study the dynamics of TCP/AQM systems. We demonstrate that the dynamics of queue and average window in Reno/RED networks are determined predominantly by the protocol stability, not by AIMD probing nor noise traffic. Our study shows that Reno/RED becomes unstable when delay increases and more strikingly, when link capacity increases. Therefore, TCP Reno is ill suited for the future high-speed network, which has motivated the design of FAST TCP. Using a continuous-time model, we prove that FAST TCP is globally stable without feedback delays and provide a sufficient condition for local stability when feedback delays are present. We also introduce a discrete-time model for FAST TCP that fully captures the effect of self-clocking and derive the local stability condition for general networks with feedback delays.</p>
<p>Second, the equilibrium properties (i.e., fairness, throughput, and capacity) of TCP/AQM systems are studied using the utility maximization framework. We quantitatively capture the variations in network throughput with changes in link capacity and allocation fairness. We clarify the open conjecture of whether a fairer allocation is always more efficient. The effects of changes in routing are studied using a joint optimization problem over both source rates and their routes. We investigate whether minimal-cost routing with proper link costs can solve this joint optimization problem in a distributed way. We also identify the tradeoff between achievable utility and routing stability.</p>
<p>At the end, two other related projects are briefly described.</p>https://thesis.library.caltech.edu/id/eprint/4530Design and Analysis of Network Codes
https://resolver.caltech.edu/CaltechETD:etd-05302006-131149
Authors: {'items': [{'email': 'jaggi@ie.cuhk.edu.hk', 'id': 'Jaggi-Sidharth', 'name': {'family': 'Jaggi', 'given': 'Sidharth'}, 'orcid': '0000-0002-5522-7486', 'show_email': 'YES'}]}
Year: 2006
DOI: 10.7907/7ERZ-H253
<p>The information theoretic aspects of large networks with many terminals present several interesting and non-intuitive phenomena. One such crucial phenomenon was first explored in a detailed manner in the excellent work by Ahlswede at al. It compared two paradigms for operating a network -- one in which interior nodes were restricted to only copying and forwarding incoming messages on outgoing links, and another in which internal nodes were allowed to perform non-trivial arithmetic operations on information on incoming links to generate information on outgoing links. It showed that the latter approach could substantially improve throughput compared to the more traditional scenario. Further work by various authors showed how to design codes (called network codes) to transmit under this new paradigm and also demonstrated exciting new phenomena for these codes such as robustness against network failures, distributed design, and increased security.</p>
<p>In this work, we consider the low-complexity design and analysis of network codes, with a focus on codes for multicasting information. We examine both centralized and decentralized design of such codes, and also both randomized and deterministic design algorithms. We compare different notions of linearity and show the interplay between these notions in the design of linear network codes. We determine bounds on the complexity of network codes. We also consider the problem of error-correction and secrecy for network codes when a malicious adversary controls some subset of the network resources.</p>https://thesis.library.caltech.edu/id/eprint/2304Distributed Averaging and Efficient File Sharing on Peer-to-Peer Networks
https://resolver.caltech.edu/CaltechETD:etd-01102007-010550
Authors: {'items': [{'email': 'mortada.mehyar@gmail.com', 'id': 'Mehyar-Mortada', 'name': {'family': 'Mehyar', 'given': 'Mortada'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/Q9EV-S167
<p>The work presented in this thesis is mainly divided in two parts. In the first part we study the problem of distributed averaging, which has attracted a lot of interest in the research community in recent years. Our work focuses on the issues of implementing distributed averaging algorithms on peer-to-peer networks such as the Internet. We present algorithms that eliminate the need for global coordination or synchronization, as many other algorithms require, and show mathematical analysis of their convergence.</p>
<p>Discrete-event simulations that verify the theoretical results are presented. We show that the algorithms proposed converge rapidly in practical scenarios. Real-world experiments are also presented to further corroborate these results. We present experiments conducted on the PlanetLab research network. Finally, we present several promising applications of distributed averaging that can be implemented in a wide range of areas of interest.</p>
<p>The second part of this thesis, also related to peer-to-peer networking, is about modelling and understanding peer-to-peer file sharing. The BitTorrent protocol has become one of the most popular peer-to-peer file sharing systems in recent years. Theoretical understanding of the global behavior of BitTorrent and similar peer-to-peer file sharing systems is however not very complete yet. We study a model that requires very simple assumptions yet exhibits a lot structure. We show that it is possible to consider a wide range of performance criteria within the framework, and that the model captures many of the important issues of peer-to-peer file sharing.</p>
<p>We believe the results provide fundamental insights to practical peer-to-peer file sharing systems. We show that many optimization criteria can be studied within our framework. Many new directions of research are also opened up.</p>https://thesis.library.caltech.edu/id/eprint/104Microscopic Behavior of Internet Congestion Control
https://resolver.caltech.edu/CaltechETD:etd-05292007-223200
Authors: {'items': [{'email': 'DavidWei@ACM.ORG', 'id': 'Wei-Xiaoliang-David', 'name': {'family': 'Wei', 'given': 'Xiaoliang (David)'}, 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/W5E3-9N04
<p>The Internet research community has focused on the macroscopic behavior of Transmission Control Protocol (TCP) and overlooked its microscopic behavior for years. This thesis studies the microscopic behavior of TCP and its effects on performance. We go into the packet-level details of TCP control algorithms and explore the behavior in short time scales within one round-trip time. We find that the burstiness effects in such small time scales have significant impacts on both delay-based TCP and loss-based TCP.</p>
<p>For delay-based TCP algorithms, the micro-burst leads to much faster queue convergence than what the traditional macroscopic models predict. With such fast queue convergence, some delay-based congestion control algorithms are much more stable in reality than in the analytical results from existing macroscopic models. This observation allows us to design more responsive yet stable algorithm which would otherwise be impossible.</p>
<p>For loss-based TCP algorithms, the sub-RTT burstiness in TCP packet transmission process has significant impacts on the loss synchronization rate, an important parameter which affects the efficiency, fairness and convergence of loss-based TCP congestion control algorithms.</p>
<p>Our findings explain several long-standing controversial problems and have inspired new algorithms that achieve better TCP performance.</p>https://thesis.library.caltech.edu/id/eprint/2252Reflection and Its Application to Mechanized MetaReasoning About Programming Languages
https://resolver.caltech.edu/CaltechETD:etd-05222007-211909
Authors: {'items': [{'id': 'Yu-Xin', 'name': {'family': 'Yu', 'given': 'Xin'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/S0HG-RT72
<p>It is well known that adding reflective reasoning can tremendously increase the power of a proof assistant. In order for this theoretical increase of power to become accessible to users in practice, the proof assistant needs to provide a great deal of infrastructure to support reflective reasoning. In this thesis we explore the problem of creating a practical implementation of such a support layer.</p>
<p>Our implementation takes a specification of a logical theory (which is identical to how it would be specified if we simply intended to reason within this logical theory, instead of reflecting it) and automatically generates the necessary definitions, lemmas, and proofs that are needed to enable the reflected metareasoning in the provided theory.</p>
<p>One of the key features of our approach is that the structure of a logic is preserved when it is reflected, including variables, meta variables, and binding structure. This allows the structure of proofs to be preserved as well, and there is a one-to-one map from proof steps in the original logic to proof steps in the reflected logic. The act of reflecting a language is automated; all definitions, theorems, and proofs are preserved by the transformation and all the key lemmas (such as proof and structural induction) are automatically derived.</p>
<p>The principal representation used by the reflected logic is higher-order abstract syntax (HOAS). However, reasoning about terms in HOAS can be awkward in some cases, especially for variables. For this reason, we define a computationally equivalent variable-free de Bruijn representation that is interchangeable with the HOAS in all contexts. The de Bruijn representation inherits the properties of substitution and alpha-equality from the logical framework, and it is not complicated by administrative issues like variable renumbering.</p>
<p>We further develop the concepts and principles of proofs, provability, and structural and proof induction. This work is fully implemented in the MetaPRL theorem prover. We illustrate with an application to [F...] as defined in the POPLmark challenge.</p>https://thesis.library.caltech.edu/id/eprint/1960Wireless Network Design and Control
https://resolver.caltech.edu/CaltechETD:etd-12282006-181735
Authors: {'items': [{'email': 'lijun.chen@colorado.edu', 'id': 'Chen-Lijun', 'name': {'family': 'Chen', 'given': 'Lijun'}, 'orcid': '0000-0001-6694-4299', 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/TEVD-PK95
<p>Optimization theory and game theory provide a suite of tools that are flexible in modelling various network systems, and a rich series of equilibrium solution concepts and convergent algorithms. In this thesis, we view network protocols as distributed algorithms achieving the corresponding network equilibria, and study wireless network design and control in optimization and game-theoretic frameworks.</p>
<p>Specifically, we first take a holistic approach and design an overall framework for the protocol architecture in ad hoc wireless networks. The goal is to integrate various protocol layers into a unified framework, by regarding them as distributed computations over the network to solve some optimization problem. Our current theory integrates three functions--congestion control, routing and scheduling--in transport, network and link layers into a coherent framework. These three functions interact through and are regulated by congestion price so as to achieve a global optimality, even in a time-varying environment. This framework is promising to be extended to provide a mathematical theory for network architecture, and to allow us to systematically carry out cross-layer design.</p>
<p>We then develop a general game-theoretic framework for contention control. We define a general game-theoretic model, called random access game, to study the contention/interaction among wireless nodes, and propose a novel medium access method derived from carrier sensing multiple access with collision avoidance in which each node estimates its conditional collision probability and adjusts its persistence probability or contention window, according to a distributed strategy update mechanism achieving the Nash equilibrium of random access game. This results in simple dynamics, controllable performance objectives, good short-term fairness, low collision, and high throughput. As wireless nodes can estimate conditional collision probabilities by observing consecutive idle slots between transmissions, we can decouple contention control from handling failed transmissions. This also opens up other opportunities such as rate adaptation to channel variations. In addition to providing a general and systematic design methodology for medium access control, the random access game model also provides an analytical framework to understand the equilibrium properties such as throughput, loss and fairness, and dynamic properties of different medium access protocols and their interactions.</p>
<p>Finally, we conclude this work with some suggestions for future research.</p>https://thesis.library.caltech.edu/id/eprint/5160Topologies of Complex Networks: Functions and Structures
https://resolver.caltech.edu/CaltechETD:etd-05282007-223415
Authors: {'items': [{'id': 'Li-Lun', 'name': {'family': 'Li', 'given': 'Lun'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/9G3P-7F13
<p>During the last decade, significant efforts have been made toward improving our understanding of the topological structures underlying complex networks and illuminating some of the intriguing large-scale properties exhibited by these systems. The dominant theme of these efforts has been on studying the graph-theoretic properties of the corresponding connectivity structures and on developing universal theories and models that transcend system-specific details and describe the different systems well in a statistical sense.</p>
<p>However, in this thesis we argue that these efforts have had limited success and are in need of substantial correction. Using a highly engineered system, the Internet, as a case study we demonstrate that networks are designed for a purpose, and ignoring that aspect or obscuring it with the use of some generic but random mechanism can result in models that misrepresent what matters for system functions. By accounting in a minimal manner for both the functional requirements and structural features inherent in the design of an engineered system, we propose an alternative, optimization-based modeling approach that highlights the necessary trade-offs between system performance and the technological and economic constraints that are crucial when designing the system. We show that our proposed approach yields network models that not only match the large-scale graph-theoretic properties of measured router-level topologies well but are also fully consistent with engineering intuition and networking reality, especially as far as their performance aspects and robustness properties are concerned. In fact, we show that our design-inspired network models can be easily distinguished from previously considered probabilistic network models and efficiently achieve the level of performance for which they were designed in the first place.</p>
<p>While this thesis focuses on the Internet, it has much broader implications for complex networks and graph theory generally. To better differentiate between different graphs that are identical in certain graph statistics, we introduce a structural metric, the s-metric, and demonstrate that it provides insights into the diversity of graphs constrained by certain common properties and sheds new light on many classic graph concepts such as the various notions of self-similarity, likelihood, and assortativity. Our s-metric clarifies much of the confusion surrounding the sensational qualitative claims in the current graph theory literature for complex networks and offers a rigorous and quantitative alternative.</p>
<p>Moreover, to examine the space of graphs that satisfy certain common properties, we propose a new approach that is based on establishing a link between two graphs if and only if one can be obtained from the other via a local transformation. Exploring the resulting connected space of graphs by dividing it into countable subspaces provides a much clearer picture on the whole space. We also show that this space of graphs has a rich and interesting structure and that some properties of the latter can be related to features of the individual graphs in this space (e.g., degree variability of a node $g$ in the space of graphs and the s-metric for g).</p>https://thesis.library.caltech.edu/id/eprint/2204Generalized Network Routing Metrics and Algorithms
https://resolver.caltech.edu/CaltechETD:etd-05302008-002429
Authors: {'items': [{'id': 'Soedarmadji-Edwin', 'name': {'family': 'Soedarmadji', 'given': 'Edwin'}, 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/Z94B2ZJD
<p>In this thesis, we introduce generalized network routing metrics that represent probability density parameters of the most popular communication channel models such as (a) the q-ary Symmetric Channel (q-SC) (b) the q-ary Erasure Channel (q-EC); (c) the Gilbert-Elliot Channel (GEC); and (d) the constrained Additive White Gaussian Noise (AWGN). The GEC is a very important for modelling correlated errors in channels such as the ubiquitous TCP/IP links and the wireless fading channels. In this thesis, we prove that channel models (a)--(d) can be used as inputs to the Generalized Dijkstra's Algorithm without resulting in any routing loop.</p>
<p>We also define our own generalized Dijkstra's algorithm that can solve a modified standard shortest path problem that features: (1) a subset of network nodes that are capable of reducing the accumulated path cost down to zero, and (2) a constraint that the cumulative cost of any feasible path must never exceed a prespecified maximum value. We call this modified problem the Gas Station Problem, and its solution the Gas Station Algorithm. The algorithm can be applied in many different areas such as: vehicle routing, project management, and most importantly, network communication.</p>
<p>We investigate various auxilliary synchronization algorithms used in popular routing protocols. Synchronization is used by routers to ensure that all routers operate on an identical routing table --- not a trivial task, considering network unreliabilities and possible malicious attacks. Our analysis produces a list of assumptions that guarantees synchronization. We also obtain the upper bounds to quantities such as transmission period, memory requirement, etc. In turn, these bounds can be used to rate network performance.</p>
<p>Finally, in a related contribution, we analyze message synchronization where a message is retransmitted only if the number of identical messages received exceeds a certain threshold. We define the Chinese Generals Problem as the problem of identifying the set of assumptions under which synchronization is guaranteed. This threshold-base message passing algorithm has the benefits of a tunable gain and a higher noise resistance.</p>
https://thesis.library.caltech.edu/id/eprint/2313On Achievable Rate Regions for Source Coding Over Networks
https://resolver.caltech.edu/CaltechETD:etd-05262009-111455
Authors: {'items': [{'email': 'weihsingu@gmail.com', 'id': 'Gu-WeiHsin', 'name': {'family': 'Gu', 'given': 'WeiHsin'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/J8JP-R695
<p>In the field of source coding over networks, a central goal is to understand the best possible performance for compressing and transmitting dependent data distributed over a network. The achievable rate region for such a network describes all link capacities that suffice to satisfy the reproduction demands. Here all the links in the networks are error-free, the data dependency is given by a joint distribution of the source random variables, and the source sequences are drawn i.i.d. according to the given source distribution. In this thesis, I study the achievable rate regions for general networks, deriving new properties for the rate regions of general network source coding problems, developing approximation algorithms to calculate these regions for particular examples, and deriving bounds on the regions for basic multi-hop and multi-path examples.</p>
<p>In the first part, I define a family of network source coding problems. That family contains all of the example networks in the literature as special cases. For the given family, I investigate abstract properties of the achievable rate regions for general networks. These properties include (1) continuity of the achievable rate regions with respect to both the source distribution and the distortion constraint vector and (2) a strong converse that implies the traditional strong converse. Those properties might be useful for studying a long-standing open question: whether a single-letter characterization of a given achievable rate region always exists.</p>
<p>In the second part, I develop a family of algorithms to approximate the achievable rate regions for some example network source coding problems based on their single-letter characterizations by using linear programming tools. Those examples contain (1) the lossless coded side information problem by Ahlswede and Korner, (2) the Wyner-Ziv rate-distortion function, and (3) the Berger et al. bound for the lossy coded side information problem. The algorithms may apply more widely to other examples.</p>
<p>In the third part, I study two basic networks of different types: the two-hop and the diamond networks. The two-hop network is a basic example of line networks with single relay node on the path from the source to the destination, and the diamond network is a basic example of multi-path networks that has two paths from the source to the destination, where each of the paths contains a relay node. I derive performance bounds for the achievable rate regions for these two networks.</p>
https://thesis.library.caltech.edu/id/eprint/5265Coding for Wireless Broadcast and Network Secrecy
https://resolver.caltech.edu/CaltechETD:etd-09062009-213639
Authors: {'items': [{'email': 'taocui@caltech.edu', 'id': 'Cui-Tao', 'name': {'family': 'Cui', 'given': 'Tao'}, 'show_email': 'NO'}]}
Year: 2010
DOI: 10.7907/JYV2-DM74
<p>In the first part of this thesis, we exploit wireless broadcast across different layers in wireless networks. The wireless channel is distinguished by its broadcast nature. Wireless broadcast provides a fertile ground to improve the efficiency of existing wireless networks and design new ones.</p>
<p>Specifically, we first consider relaying strategies for memoryless two-way relay channels at the physical layer. We generalize networking layer network coding operating on a finite field to physical layer network coding, which is a mapping from the relay's received signal to its transmitted signal. We analyze the symbol-error performance of several relay strategies, and optimize the relay function via functional analysis. Our results indicate that the interference caused by wireless broadcast can be exploited to improve the spectrum efficiency.</p>
<p>We then develop a cross-layer framework with wireless broadcast, which integrates rate control, network coding and scheduling in transport, network and link layers. Under the primary interference model, we show that the link scheduling problem is the maximum weighted hypergraph matching problem, which is NP-complete. We propose several distributed approximation algorithms and bound their worst case performance.</p>
<p>Next, we describe a new class of medium access control (MAC) protocol, which uses successive interference cancelation to resolve packet collision due to wireless broadcast. Each user is allowed to transmit at different data rates chosen randomly from an appropriately determined set of rates. We characterize the throughput of the proposed protocol compared to that with a centralized controller. A game-theoretic framework along with the dynamic algorithms is proposed to achieve the desired throughput optimal equilibrium, which provides a valuable perspective to understand existing MAC protocols and a general framework to design new ones to improve the system performance.</p>
<p>In the second part of this thesis, we consider the problem of secure transmission in the presence of a wiretapper. Due to wireless broadcast, wireless signals are particularly easy to jam and intercept. We derive the secrecy capacity region for the case when the location of the wiretapped links is known and propose several achievable strategies for the case when such information is unknown. We give an example to show that the secrecy capacities of the two cases are generally unequal and show that in both cases computing the secrecy capacity is NP-complete.</p>
https://thesis.library.caltech.edu/id/eprint/5279Network Coding for Resource Optimization and Error Correction
https://resolver.caltech.edu/CaltechTHESIS:06012010-161706139
Authors: {'items': [{'email': 'kim.sukwon@gmail.com', 'id': 'Kim-Sukwon', 'name': {'family': 'Kim', 'given': 'Sukwon'}, 'show_email': 'YES'}]}
Year: 2010
DOI: 10.7907/9E6W-SN15
<p>In the first part of this thesis, we demonstrate the benefits of network coding for optimizing the use of various network resources.</p>
<p>We first study the problem of minimizing the power consumption for wireless multiple unicasts. A simple XOR-based coding strategy is considered for reducing the power consumption. We present a centralized polynomial time algorithm that approximately minimizes the number of transmissions for two unicast sessions. We extend it to a greedy algorithm for general problem of multiple unicasts.</p>
<p>Previous results on network coding for low-power wireless transmissions of multiple unicasts rely on opportunistic coding or centralized optimization to reduce the power consumption. Thus we propose a distributed strategy for reducing the power consumption with wireless multiple unicasts. Our strategy attempts to increase network coding opportunities without the overhead required for centralized design or coordination. We present a polynomial time algorithm using our strategy that maximizes the expected power savings with respect to the random choice of sources and sinks on the wireless rectangular grid.</p>
<p>We study the problem of minimum-energy multicast using network coding in mobile ad hoc networks (MANETs). The optimal subgraph can be obtained by solving a linear program every time slot, but it leads to high computational complexity. We present a low-complexity approach, network coding with periodic recomputation, which recomputes an approximate solution at fixed time intervals, and uses this solution during each time interval. We analyze the power consumption and the complexity of network with this approach.</p>
<p>Recently, several back-pressure type optimization algorithms with network coding are presented for multiple unicasts and multicast. Such algorithms are distributed since decisions are made locally at each node based on feedback about the size of queues at the destination node of each link. We develop a back-pressure based distributed optimization framework, which can be used for optimizing over any class of network codes. Our approach is to specify the class of coding operations by a set of generalized links, and to develop optimization tools that apply to any network composed of such generalized links.</p>
<p>In the second part of this thesis, we study the capacity of single-source single-sink noiseless networks under adversarial attack on no more than z edges. Unlike prior papers, which assume equal capacities on all links, we allow arbitrary link capacities. Results include new upper bounds, general transmission strategies, and example networks where those bounds are tight. We introduce a new method for finding upper bounds on the linear coding capacities of arbitrary networks and show that there exists networks where the capacity is 50% greater than the best rate that can be achieved with linear coding. We also demonstrate examples where, unlike the equal link capacity case, it is necessary for intermediate nodes to do coding, nonlinear error detection or error correction in order to achieve the capacity. We introduce a new strategy called "guess-and-forward" and employ this strategy on a sequence of networks designed to provide increasingly complex generalizations of the cut-set bounds. The first is a two-node network with multiple feedback links. The second is a four-node acyclic network. The third is a family of 'zig-zag' networks. In the first two cases, the guess-and-forward strategy achieves the capacity. For zig-zag networks, we derive a achievable rate of guess-and-forward strategy.</p>https://thesis.library.caltech.edu/id/eprint/5904On Matrix Factorization and Scheduling for Finite-Time Average-Consensus
https://resolver.caltech.edu/CaltechTHESIS:05022010-193157687
Authors: {'items': [{'email': 'kokevin@gmail.com', 'id': 'Ko-Chih-Kai', 'name': {'family': 'Ko', 'given': 'Chih-Kai'}, 'show_email': 'NO'}]}
Year: 2010
DOI: 10.7907/GCT7-5Y66
We study the problem of communication scheduling for finite-time average-consensus in arbitrary connected networks. Viewing this consensus problem as a factorization of 1/n 11<sup>T</sup> by network-admissible families of matrices, we prove the existence of finite factorizations, provide scheduling algorithms for finite-time average consensus, and derive almost tight lower bounds on the size of the minimal factorization.https://thesis.library.caltech.edu/id/eprint/5763Random Matrix Recursions in Estimation, Control, and Adaptive Filtering
https://resolver.caltech.edu/CaltechTHESIS:06022011-214438378
Authors: {'items': [{'email': 'avakili@caltech.edu', 'id': 'Vakili-Ali', 'name': {'family': 'Vakili', 'given': 'Ali'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/HCKN-7W53
<p>This dissertation is devoted to the study of estimation and control over systems that can be described by linear time-varying state-space models. Examples of such systems are encountered frequently in systems theory, e.g., wireless sensor networks, adaptive filtering, distributed control, etc. Recent developments in distributed catastrophe surveillance, smart transportation, and power grid control systems further motivate such a study.</p>
<p>While linear time-invariant systems are well-understood, there is no general theory that captures various aspects of time-varying counterparts. With little exception, tackling these problems normally boils down to studying time-varying linear or non-linear recursive matrix equations, known as Lyapunov and Riccati recursions that are notoriously hard to analyze. We employ the theory of random matrices to elucidate different facets of these recursions and answer several important questions about the performance, stability, and convergence of estimation and control over such systems.</p>
<p>We make two general assumptions. First, we assume that the coefficient matrices are drawn from jointly stationary matrix-valued random processes. The stationarity assumption hardly restricts the analysis since almost all cases of practical interest fall into this category. We further assume that the state vector size, n, is relatively large. The law of large numbers however guarantees fast convergence to the asymptotic results for n being as small as 10. Under these assumptions, we develop a framework capable of characterizing steady-state and transient behavior of adaptive filters and control and estimation over communication networks. This framework proves promising by successfully tackling several problems for the first time in the literature.</p>
<p>We first study random Lyapunov recursions and characterize their transient and steady-state behavior. Lyapunov recursions appear in several classes of adaptive filters and also as lower bounds of random Riccati recursions in distributed Kalman filtering. We then look at random Riccati recursions whose nonlinearity makes them much more complicated to study. We investigate standard recursive-least-squares (RLS) filtering and extend our analysis beyond the standard case to filtering with multiple measurements, as well as the case of intermittent measurements. Finally, we study Kalman filtering with intermittent observations, which is frequently used to model wireless sensor networks. In all of these cases we obtain interesting universal laws that depend on the structure of the problem, rather than specific model parameters. We verify the accuracy of our results through various simulations for systems with as few as 10 states.</p>
https://thesis.library.caltech.edu/id/eprint/6495Systematic Design and Formal Verification of Multi-Agent Systems
https://resolver.caltech.edu/CaltechTHESIS:05232011-013046516
Authors: {'items': [{'email': 'cetta@caltech.edu', 'id': 'Pilotto-Concetta', 'name': {'family': 'Pilotto', 'given': 'Concetta'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/SCQF-VP66
<p>This thesis presents methodologies for verifying the correctness of multi-agent systems operating in hostile environments. Verification of these systems is challenging because of their inherent concurrency and unreliable communication medium. The problem is exacerbated if the model representing the multi-agent system includes infinite or uncountable data types.</p>
<p>We first consider message-passing multi-agent systems operating over an unreliable communication medium. We assume that messages in transit may be lost, delayed or received out-of-order. We present conditions on the system that reduce the design and verification of a message-passing system to the design and verification of the corresponding shared-state system operating in a friendly environment. Our conditions can be applied both to discrete and continuous agent trajectories.</p>
<p>We apply our results to verify a general class of multi-agent system whose goal is solving a system of linear equations. We discuss this class in detail and show that mobile robot linear pattern-formation schemes are instances of this class. In these protocols, the goal of the team of robots is to reach a given pattern formation.</p>
<p>We present a framework that allows verification of message-passing systems operating over an unreliable communication medium. This framework is implemented as a library of PVS theorem prover meta-theories and is built on top of the timed automata framework. We discuss the applicability of this tool. As an example, we automatically check correctness of the mobile robot linear pattern formation protocols.</p>
<p>We conclude with an analysis of the verification of multi-agent systems operating in hostile environments. Under these more general assumptions, we derive conditions on the agents' protocols and properties of the environment that ensure bounded steady-state system error. We apply these results to message-passing multi-agent systems that allow for lost, delayed, received out-of-order or forged messages, and to multi-agent systems whose goal is tracking time-varying quantities. We show that pattern formation schemes are robust to leaders dynamics, i.e., in these schemes, followers eventually form the pattern defined by the new positions of the leaders.</p>https://thesis.library.caltech.edu/id/eprint/6418Large-Scale Complex Systems: From Antenna Circuits to Power Grids
https://resolver.caltech.edu/CaltechTHESIS:05132011-113642762
Authors: {'items': [{'email': 'lavaei@cds.caltech.edu', 'id': 'Lavaeiyanesi-Javad', 'name': {'family': 'Lavaei', 'given': 'Javad'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/CM46-5R54
<p>This dissertation is motivated by the lack of scalable methods for the analysis and synthesis of different large-scale complex systems appearing in electrical and computer engineering. The systems of interest in this work are power networks, analog circuits, antenna systems, communication networks and distributed control systems. By combining theories from control and optimization, the high-level objective is to develop new design tools and algorithms that explicitly exploit the physical properties of these practical systems (e.g., passivity of electrical elements or sparsity of network topology). To this end, the aforementioned systems are categorized intro three classes of systems, and then studied in Parts I, II, and III of this dissertation, as explained below:</p>
<p>Power networks: In Part I of this work, the operation planning of power networks using efficient algorithms is studied. The primary focus is on the optimal power flow (OPF) problem, which has been studied by the operations research and power communities in the past 50 years with little success. In this part, it is shown that there exists an efficient method to solve a practical OPF problem along with many other energy-related optimization problems such as dynamic OPF or security-constrained OPF. The main reason for the successful convexification of these optimization problems is also identified to be the physical properties of a power circuit, especially the passivity of transmission lines.</p>
<p>Circuits and systems: Motivated by different applications in power networks, electromagnetics and optics, Part II of this work studies the fundamental limits associated with the synthesis of a particular type of linear circuit. It is shown that the optimal design of the parameters of this type of circuit can be performed in polynomial time if the circuit is passive and there are sufficient number of controllable (unknown) parameters. This result introduces a trade-off between the design simplicity and the implementation complexity for an important class of linear circuits. As an application of this methodology, the design of smart antennas is also studied; the goal is to devise an intelligent wireless communication device in order to avoid co-channel interference, power consumption in undesired directions and security issues. Since the existing smart antennas are either hard to program or hard to implement, a new type of smart antenna is synthesized by utilizing tools from algebraic geometry, control, communications, and circuits, which is both easy to program and easy to implement.</p>
<p>Distributed computation: The first problem tackled in Part III of this work is a very simple type of distributed computation, referred to as quantized consensus, which aims to compute the average of a set of numbers using a distributed algorithm subject to a quantization error. It is shown that quantized consensus is reached by means of a recently proposed gossip algorithm, and the convergence time of the algorithm is also derived. The second problem studied in Part III is a more advanced type of distributed computation, which is the distributed resource allocation problem for the Internet. The existing distributed resource allocation algorithms aim to maximize the utility of the network only at the equilibrium point and ignore the transient behavior of the network. To address this issue, it is shown that optimal control theory provides powerful tools for designing distributed resource allocation algorithms with a guaranteed real-time performance.</p>
<p>The results of this work can all be integrated to address real-world interdisciplinary problems, such as the design of the next generation of the electrical power grid, named the Smart Grid.</p>
https://thesis.library.caltech.edu/id/eprint/6391Peer Effects in Social Networks: Search, Matching Markets, and Epidemics
https://resolver.caltech.edu/CaltechTHESIS:05222012-145639265
Authors: {'items': [{'email': 'eabodine@gmail.com', 'id': 'Bodine-Baron-Elizabeth-Anne', 'name': {'family': 'Bodine-Baron', 'given': 'Elizabeth Anne'}, 'show_email': 'NO'}]}
Year: 2012
DOI: 10.7907/GDV2-YF12
<p>Social network analysis emerged as an important area in sociology in the early 1930s, marking a shift from looking at individual attribute data to examining the relationships between people and groups. Surveying many different types of real-world networks, researchers quickly found that different types of social networks tend to share a common set of structural characteristics, including small diameter, high clustering, and heavy-tailed degree distributions. Moving beyond real networks, in the 1990s researchers began to propose random network models to explain these commonly observed social network structures. These models laid the foundation for investigation into problems where the underlying network plays a key role, from the spread of information and disease, to the design of distributed communication and search algorithms, to mechanism design and public policy. Here we focus on the role of peer effects in social networks. Through this lens, we develop a mathematically tractable random network model incorporating searchability, propose a novel way to model and analyze two-sided matching markets with externalities, model and calculate the cost of an epidemic spreading on a complex network, and examine the impact of conforming and non-conforming peer effects in vaccination decisions on public health policy.</p>
<p>Throughout this work, the goal is to bring together knowledge and techniques from diverse fields like sociology, engineering, and economics, exploiting our understanding of social network structure and generative models to understand deeper problems that — without this knowledge — could be intractable. Instead of crippling our analysis, social network characteristics allow us to reach deeper insights about the interaction between a particular problem and the network underlying it.</p>https://thesis.library.caltech.edu/id/eprint/7064Scheduling for Heavy-Tailed and Light-Tailed Workloads in Queueing Systems
https://resolver.caltech.edu/CaltechTHESIS:06012012-134536732
Authors: {'items': [{'email': 'jayakrishnan.u@gmail.com', 'id': 'Nair-Jayakrishnan-U', 'name': {'family': 'Nair', 'given': 'Jayakrishnan U.'}, 'show_email': 'YES'}]}
Year: 2012
DOI: 10.7907/AAXJ-EX10
<p>In much of classical queueing theory, workloads are assumed to be light-tailed, with job sizes being described using exponential or phase type distributions. However, over the past two decades, studies have shown that several real-world workloads exhibit heavy-tailed characteristics. As a result, there has been a strong interest in studying queues with heavy-tailed workloads. So at this stage, there is a large body of literature on queues with light-tailed workloads, and a large body of literature on queues with heavy-tailed workloads. However, heavy-tailed workloads and light-tailed workloads differ considerably in their behavior, and these two types of workloads are rarely studied jointly.</p>
<p>In this thesis, we design scheduling policies for queueing systems, considering both heavy-tailed as well as light-tailed workloads. The motivation for this line of work is twofold. First, since real world workloads can be heavy-tailed or light-tailed, it is desirable to design schedulers that are robust in their performance to distributional assumptions on the workload. Second, there might be scenarios where a heavy-tailed and a light-tailed workload interact in a queueing system. In such cases, it is desirable to design schedulers that guarantee fairness in resource allocation for both workload types.</p>
<p>In this thesis, we study three models involving the design of scheduling disciplines for both heavy-tailed as well as light-tailed workloads. In Chapters 3 and 4, we design schedulers that guarantee robust performance across heavy-tailed and light-tailed workloads. In Chapter 5, we consider a setting in which a heavy-tailed and a light-tailed workload complete for service. In this setting, we design scheduling policies that guarantee good response time tail performance for both workloads, while also maintaining throughput optimality.</p>https://thesis.library.caltech.edu/id/eprint/7121On Erasure Coding for Distributed Storage and Streaming Communications
https://resolver.caltech.edu/CaltechTHESIS:05312013-162820930
Authors: {'items': [{'email': 'leong.derek@gmail.com', 'id': 'Leong-Derek', 'name': {'family': 'Leong', 'given': 'Derek'}, 'show_email': 'NO'}]}
Year: 2013
DOI: 10.7907/PZJ8-F333
<p>The work presented in this thesis revolves around erasure correction coding, as applied to distributed data storage and real-time streaming communications.</p>
<p>First, we examine the problem of allocating a given storage budget over a set of nodes for maximum reliability.
The objective is to find an allocation of the budget that maximizes the probability of successful recovery by a data collector accessing a random subset of the nodes.
This optimization problem is challenging in general because of its combinatorial nature, despite its simple formulation.
We study several variations of the problem, assuming different allocation models and access models, and determine the optimal allocation and the optimal symmetric allocation (in which all nonempty nodes store the same amount of data) for a variety of cases.
Although the optimal allocation can have nonintuitive structure and can be difficult to find in general, our results suggest that, as a simple heuristic, reliable storage can be achieved by spreading the budget maximally over all nodes when the budget is large, and spreading it minimally over a few nodes when it is small.
Coding would therefore be beneficial in the former case, while uncoded replication would suffice in the latter case.</p>
<p>Second, we study how distributed storage allocations affect the recovery delay in a mobile setting.
Specifically, two recovery delay optimization problems are considered for a network of mobile storage nodes:
the maximization of the probability of successful recovery by a given deadline, and the minimization of the expected recovery delay.
We show that the first problem is closely related to the earlier allocation problem, and solve the second problem completely for the case of symmetric allocations.
It turns out that the optimal allocations for the two problems can be quite different.
In a simulation study, we evaluated the performance of a simple data dissemination and storage protocol for mobile delay-tolerant networks, and observed that the choice of allocation can have a significant impact on the recovery delay under a variety of scenarios.</p>
<p>Third, we consider a real-time streaming system where messages created at regular time intervals at a source are encoded for transmission to a receiver over a packet erasure link;
the receiver must subsequently decode each message within a given delay from its creation time.
For erasure models containing a limited number of erasures per coding window, per sliding window, and containing erasure bursts whose maximum length is sufficiently short or long, we show that a time-invariant intrasession code asymptotically achieves the maximum message size among all codes that allow decoding under all admissible erasure patterns.
For the bursty erasure model, we also show that diagonally interleaved codes derived from specific systematic block codes are asymptotically optimal over all codes in certain cases.
We also study an i.i.d. erasure model in which each transmitted packet is erased independently with the same probability;
the objective is to maximize the decoding probability for a given message size.
We derive an upper bound on the decoding probability for any time-invariant code, and show that the gap between this bound and the performance of a family of time-invariant intrasession codes is small when the message size and packet erasure probability are small.
In a simulation study, these codes performed well against a family of random time-invariant convolutional codes under a number of scenarios.</p>
<p>Finally, we consider the joint problems of routing and caching for named data networking.
We propose a backpressure-based policy that employs virtual interest packets to make routing and caching decisions.
In a packet-level simulation, the proposed policy outperformed a basic protocol that combines shortest-path routing with least-recently-used (LRU) cache replacement.</p>https://thesis.library.caltech.edu/id/eprint/7806Mathematical Study of Complex Networks: Brain, Internet, and Power Grid
https://resolver.caltech.edu/CaltechTHESIS:05252013-081655550
Authors: {'items': [{'email': 'sojoudi_s@yahoo.com', 'id': 'Sojoudi-Somayeh', 'name': {'family': 'Sojoudi', 'given': 'Somayeh'}, 'show_email': 'NO'}]}
Year: 2013
DOI: 10.7907/E750-2M74
<p>The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.</p>
<p>Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.</p>
<p>Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.</p>
<p>Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.</p>
<p>Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.</p>
<p>Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.</p>https://thesis.library.caltech.edu/id/eprint/7753Distributed Optimization in Power Networks and General Multi-agent Systems
https://resolver.caltech.edu/CaltechTHESIS:05312013-122007615
Authors: {'items': [{'email': 'lina.mtbi2003@gmail.com', 'id': 'Li-Na-Lina', 'name': {'family': 'Li', 'given': 'Na (Lina)'}, 'show_email': 'YES'}]}
Year: 2013
DOI: 10.7907/NHVJ-FX37
<p>The dissertation studies the general area of complex networked systems that consist of interconnected and active heterogeneous components and usually operate in uncertain environments and with incomplete information. Problems associated with those systems are typically large-scale and computationally intractable, yet they are also very well-structured and have features that can be exploited by appropriate modeling and computational methods. The goal of this thesis is to develop foundational theories and tools to exploit those structures that can lead to computationally-efficient and distributed solutions, and apply them to improve systems operations and architecture.</p>
<p>Specifically, the thesis focuses on two concrete areas. The first one is to design distributed rules to manage distributed energy resources in the power network. The power network is undergoing a fundamental transformation. The future smart grid, especially on the distribution system, will be a large-scale network of distributed energy resources (DERs), each introducing random and rapid fluctuations in power supply, demand, voltage and frequency. These DERs provide a tremendous opportunity for sustainability, efficiency, and power reliability. However, there are daunting technical challenges in managing these DERs and optimizing their operation. The focus of this dissertation is to develop scalable, distributed, and real-time control and optimization to achieve system-wide efficiency, reliability, and robustness for the future power grid. In particular, we will present how to explore the power network structure to design efficient and distributed market and algorithms for the energy management. We will also show how to connect the algorithms with physical dynamics and existing control mechanisms for real-time control in power networks.</p>
<p>The second focus is to develop distributed optimization rules for general multi-agent engineering systems. A central goal in multiagent systems is to design local control laws for the individual agents to ensure that the emergent global behavior is desirable with respect to the given system level objective. Ideally, a system designer seeks to satisfy this goal while conditioning each agent’s control on the least amount of information possible. Our work focused on achieving this goal using the framework of game theory. In particular, we derived a systematic methodology for designing local agent objective functions that guarantees (i) an equivalence between the resulting game-theoretic equilibria and the system level design objective and (ii) that the resulting game possesses an inherent structure that can be exploited for distributed learning, e.g., potential games. The control design can then be completed by applying any distributed learning algorithm that guarantees convergence to the game-theoretic equilibrium. One main advantage of this game theoretic approach is that it provides a hierarchical decomposition between the decomposition of the systemic objective (game design) and the specific local decision rules (distributed learning algorithms). This decomposition provides the system designer with tremendous flexibility to meet the design objectives and constraints inherent in a broad class of multiagent systems. Furthermore, in many settings the resulting controllers will be inherently robust to a host of uncertainties including asynchronous clock rates, delays in information, and component failures.</p>https://thesis.library.caltech.edu/id/eprint/7791Algorithmic Challenges in Green Data Centers
https://resolver.caltech.edu/CaltechTHESIS:05312013-223354639
Authors: {'items': [{'email': 'linmhcs@gmail.com', 'id': 'Lin-Minghong', 'name': {'family': 'Lin', 'given': 'Minghong'}, 'show_email': 'NO'}]}
Year: 2013
DOI: 10.7907/NRXJ-JB76
With data centers being the supporting infrastructure for a wide range of IT services, their efficiency has become a big concern to operators, as well as to society, for both economic and environmental reasons. The goal of this thesis is to design energy-efficient algorithms that reduce energy cost while minimizing compromise to service. We focus on the algorithmic challenges at different levels of energy optimization across the data center stack. The algorithmic challenge at the device level is to improve the energy efficiency of a single computational device via techniques such as job scheduling and speed scaling. We analyze the common speed scaling algorithms in both the worst-case model and stochastic model to answer some fundamental issues in the design of speed scaling algorithms. The algorithmic challenge at the local data center level is to dynamically allocate resources (e.g., servers) and to dispatch the workload in a data center. We develop an online algorithm to make a data center more power-proportional by dynamically adapting the number of active servers. The algorithmic challenge at the global data center level is to dispatch the workload across multiple data centers, considering the geographical diversity of electricity price, availability of renewable energy, and network propagation delay. We propose algorithms to jointly optimize routing and provisioning in an online manner. Motivated by the above online decision problems, we move on to study a general class of online problem named "smoothed online convex optimization", which seeks to minimize the sum of a sequence of convex functions when "smooth" solutions are preferred. This model allows us to bridge different research communities and help us get a more fundamental understanding of general online decision problems.https://thesis.library.caltech.edu/id/eprint/7815On Delay and Security in Network Coding
https://resolver.caltech.edu/CaltechTHESIS:09292012-041022964
Authors: {'items': [{'email': 'tdikal@gmail.com', 'id': 'Dikaliotis-Theodoros-K', 'name': {'family': 'Dikaliotis', 'given': 'Theodoros K.'}, 'show_email': 'NO'}]}
Year: 2013
DOI: 10.7907/1KE1-DW91
<p>In this thesis, delay and security issues in network coding are considered. First, we study the delay incurred in the transmission of a fixed number of packets through acyclic networks comprised of erasure links. The two transmission schemes studied are routing with hop-by-hop retransmissions, where every node in the network simply stores and forwards its received packets, and linear coding, where nodes mix their packets by forwarding linear combinations of all their previously received packets. We show that even though the achievable rates of coding and routing are the same, network coding can have an increasingly better performance than routing as the number of packets increases.</p>
<p>Secondly, we investigate the security benefits of network coding. We investigate the achievable secrecy rate region in a general network of noisy wiretap channels with general communication demands. The eavesdropper has access to an unknown set of links, and on the wiretapped links observes a degraded version of the intended receiver's observation. While characterizing the capacity in general is an open problem, in the noise-free case there exist inner and outer bounds. In the noisy case, we show how one can change any of the wiretap channels to a noiseless degraded broadcast channel, so that the derived network's rate region bounds, and under certain conditions is equivalent, to that of the initial network. Specifically, we showed that in case the eavesdropper can choose only a single link to wiretap at each time, then one can change all the links in the network with corresponding noiseless ones, creating an equivalent noiseless secrecy problem. In the case where the eavesdropper can wiretap multiple links simultaneously, we derive upper and lower bounding noiseless network problems.</p>
<p>Finally, we consider design practical code design for the detection of adversarial errors in a distributed storage system. We build on work of functions that can fool linear polynomials to create and communicate hash functions of the data in order to detect with high probability the maliciously attacked nodes in the system.</p>https://thesis.library.caltech.edu/id/eprint/7217Optimal Uncertainty Quantification via Convex Optimization and Relaxation
https://resolver.caltech.edu/CaltechTHESIS:10162013-111333269
Authors: {'items': [{'email': 'hanshuo99@gmail.com', 'id': 'Han-Shuo', 'name': {'family': 'Han', 'given': 'Shuo'}, 'show_email': 'NO'}]}
Year: 2014
DOI: 10.7907/X00K-T615
<p>Many engineering applications face the problem of bounding the expected value of a quantity of interest (performance, risk, cost, etc.) that depends on stochastic uncertainties whose probability distribution is not known exactly. Optimal uncertainty quantification (OUQ) is a framework that aims at obtaining the best bound in these situations by explicitly incorporating available information about the distribution. Unfortunately, this often leads to non-convex optimization problems that are numerically expensive to solve.</p>
<p>This thesis emphasizes on efficient numerical algorithms for OUQ problems. It begins by investigating several classes of OUQ problems that can be reformulated as convex optimization problems. Conditions on the objective function and information constraints under which a convex formulation exists are presented. Since the size of the optimization problem can become quite large, solutions for scaling up are also discussed. Finally, the capability of analyzing a practical system through such convex formulations is demonstrated by a numerical example of energy storage placement in power grids.</p>
<p>When an equivalent convex formulation is unavailable, it is possible to find a convex problem that provides a meaningful bound for the original problem, also known as a convex relaxation. As an example, the thesis investigates the setting used in Hoeffding's inequality. The naive formulation requires solving a collection of non-convex polynomial optimization problems whose number grows doubly exponentially. After structures such as symmetry are exploited, it is shown that both the number and the size of the polynomial optimization problems can be reduced significantly. Each polynomial optimization problem is then bounded by its convex relaxation using sums-of-squares. These bounds are found to be tight in all the numerical examples tested in the thesis and are significantly better than Hoeffding's bounds.</p>https://thesis.library.caltech.edu/id/eprint/7991Sustainable IT and IT for Sustainability
https://resolver.caltech.edu/CaltechTHESIS:05312014-215801543
Authors: {'items': [{'email': 'zhenhua02@gmail.com', 'id': 'Liu-Zhenhua', 'name': {'family': 'Liu', 'given': 'Zhenhua'}, 'show_email': 'YES'}]}
Year: 2014
DOI: 10.7907/296T-HR79
<p>Energy and sustainability have become one of the most critical issues of our generation. While the abundant potential of renewable energy such as solar and wind provides a real opportunity for sustainability, their intermittency and uncertainty present a daunting operating challenge. This thesis aims to develop analytical models, deployable algorithms, and real systems to enable efficient integration of renewable energy into complex distributed systems with limited information.</p>
<p>The first thrust of the thesis is to make IT systems more sustainable by facilitating the integration of renewable energy into these systems. IT represents the fastest growing sectors in energy usage and greenhouse gas pollution. Over the last decade there are dramatic improvements in the energy efficiency of IT systems, but the efficiency improvements do not necessarily lead to reduction in energy consumption because more servers are demanded. Further, little effort has been put in making IT more sustainable, and most of the improvements are from improved "engineering" rather than improved "algorithms". In contrast, my work focuses on developing algorithms with rigorous theoretical analysis that improve the sustainability of IT. In particular, this thesis seeks to exploit the flexibilities of cloud workloads both (i) in time by scheduling delay-tolerant workloads and (ii) in space by routing requests to geographically diverse data centers. These opportunities allow data centers to adaptively respond to renewable availability, varying cooling efficiency, and fluctuating energy prices, while still meeting performance requirements. The design of the enabling algorithms is however very challenging because of limited information, non-smooth objective functions and the need for distributed control. Novel distributed algorithms are developed with theoretically provable guarantees to enable the "follow the renewables" routing. Moving from theory to practice, I helped HP design and implement industry's first Net-zero Energy Data Center. </p>
<p>The second thrust of this thesis is to use IT systems to improve the sustainability and efficiency of our energy infrastructure through data center demand response. The main challenges as we integrate more renewable sources to the existing power grid come from the fluctuation and unpredictability of renewable generation. Although energy storage and reserves can potentially solve the issues, they are very costly. One promising alternative is to make the cloud data centers demand responsive. The potential of such an approach is huge. </p>
<p>To realize this potential, we need adaptive and distributed control of cloud data centers and new electricity market designs for distributed electricity resources. My work is progressing in both directions. In particular, I have designed online algorithms with theoretically guaranteed performance for data center operators to deal with uncertainties under popular demand response programs. Based on local control rules of customers, I have further designed new pricing schemes for demand response to align the interests of customers, utility companies, and the society to improve social welfare.</p>https://thesis.library.caltech.edu/id/eprint/8457An Integrated Design Approach to Power Systems: From Power Flows to Electricity Markets
https://resolver.caltech.edu/CaltechTHESIS:06012014-040224456
Authors: {'items': [{'email': 'subhonmesh.bose@gmail.com', 'id': 'Bose-Subhonmesh', 'name': {'family': 'Bose', 'given': 'Subhonmesh'}, 'show_email': 'NO'}]}
Year: 2014
DOI: 10.7907/FRGW-AF26
Power system is at the brink of change. Engineering needs, economic forces and environmental factors are the main drivers of this change. The vision is to build a smart electrical grid and a smarter market mechanism around it to fulfill mandates on clean energy. Looking at engineering and economic issues in isolation is no longer an option today; it needs an integrated design approach. In this thesis, I shall revisit some of the classical questions on the engineering operation of power systems that deals with the nonconvexity of power flow equations. Then I shall explore some issues of the interaction of these power flow equations on the electricity markets to address the fundamental issue of market power in a deregulated market environment. Finally, motivated by the emergence of new storage technologies, I present an interesting result on the investment decision problem of placing storage over a power network. The goal of this study is to demonstrate that modern optimization and game theory can provide unique insights into this complex system. Some of the ideas carry over to applications beyond power systems.https://thesis.library.caltech.edu/id/eprint/8458Distributed Load Control in Multiphase Radial Networks
https://resolver.caltech.edu/CaltechTHESIS:01272015-214848277
Authors: {'items': [{'email': 'ganlingwen@gmail.com', 'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}, 'show_email': 'YES'}]}
Year: 2015
DOI: 10.7907/Z9FQ9TJ0
<p>The current power grid is on the cusp of modernization due to the emergence of distributed generation and controllable loads, as well as renewable energy. On one hand, distributed and renewable generation is volatile and difficult to dispatch. On the other hand, controllable loads provide significant potential for compensating for the uncertainties. In a future grid where there are thousands or millions of controllable loads and a large portion of the generation comes from volatile sources like wind and solar, distributed control that shifts or reduces the power consumption of electric loads in a reliable and economic way would be highly valuable.</p>
<p>Load control needs to be conducted with network awareness. Otherwise, voltage violations and overloading of circuit devices are likely. To model these effects, network power flows and voltages have to be considered explicitly. However, the physical laws that determine power flows and voltages are nonlinear. Furthermore, while distributed generation and controllable loads are mostly located in distribution networks that are multiphase and radial, most of the power flow studies focus on single-phase networks.</p>
<p>This thesis focuses on distributed load control in multiphase radial distribution networks. In particular, we first study distributed load control without considering network constraints, and then consider network-aware distributed load control.</p>
<p>Distributed implementation of load control is the main challenge if network constraints can be ignored. In this case, we first ignore the uncertainties in renewable generation and load arrivals, and propose a distributed load control algorithm, Algorithm 1, that optimally schedules the deferrable loads to shape the net electricity demand. Deferrable loads refer to loads whose total energy consumption is fixed, but energy usage can be shifted over time in response to network conditions. Algorithm 1 is a distributed gradient decent algorithm, and empirically converges to optimal deferrable load schedules within 15 iterations.</p>
<p>We then extend Algorithm 1 to a real-time setup where deferrable loads arrive over time, and only imprecise predictions about future renewable generation and load are available at the time of decision making. The real-time algorithm Algorithm 2 is based on model-predictive control: Algorithm 2 uses updated predictions on renewable generation as the true values, and computes a pseudo load to simulate future deferrable load. The pseudo load consumes 0 power at the current time step, and its total energy consumption equals the expectation of future deferrable load total energy request.</p>
<p>Network constraints, e.g., transformer loading constraints and voltage regulation constraints, bring significant challenge to the load control problem since power flows and voltages are governed by nonlinear physical laws. Remarkably, distribution networks are usually multiphase and radial. Two approaches are explored to overcome this challenge: one based on convex relaxation and the other that seeks a locally optimal load schedule.</p>
<p>To explore the convex relaxation approach, a novel but equivalent power flow model, the branch flow model, is developed, and a semidefinite programming relaxation, called BFM-SDP, is obtained using the branch flow model. BFM-SDP is mathematically equivalent to a standard convex relaxation proposed in the literature, but numerically is much more stable. Empirical studies show that BFM-SDP is numerically exact for the IEEE 13-, 34-, 37-, 123-bus networks and a real-world 2065-bus network, while the standard convex relaxation is numerically exact for only two of these networks.</p>
<p>Theoretical guarantees on the exactness of convex relaxations are provided for two types of networks: single-phase radial alternative-current (AC) networks, and single-phase mesh direct-current (DC) networks. In particular, for single-phase radial AC networks, we prove that a second-order cone program (SOCP) relaxation is exact if voltage upper bounds are not binding; we also modify the optimal load control problem so that its SOCP relaxation is always exact. For single-phase mesh DC networks, we prove that an SOCP relaxation is exact if 1) voltage upper bounds are not binding, or 2) voltage upper bounds are uniform and power injection lower bounds are strictly negative; we also modify the optimal load control problem so that its SOCP relaxation is always exact.</p>
<p>To seek a locally optimal load schedule, a distributed gradient-decent algorithm, Algorithm 9, is proposed. The suboptimality gap of the algorithm is rigorously characterized and close to 0 for practical networks. Furthermore, unlike the convex relaxation approach, Algorithm 9 ensures a feasible solution. The gradients used in Algorithm 9 are estimated based on a linear approximation of the power flow, which is derived with the following assumptions: 1) line losses are negligible; and 2) voltages are reasonably balanced. Both assumptions are satisfied in practical distribution networks. Empirical results show that Algorithm 9 obtains 70+ times speed up over the convex relaxation approach, at the cost of a suboptimality within numerical precision.</p>https://thesis.library.caltech.edu/id/eprint/8762Distributed Control and Optimization for Communication and Power Systems
https://resolver.caltech.edu/CaltechTHESIS:01262016-194420781
Authors: {'items': [{'email': 'qiuyupeng@gmail.com', 'id': 'Peng-Qiuyu', 'name': {'family': 'Peng', 'given': 'Qiuyu'}, 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z99C6VBW
<p>We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.</p>
<p>This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.</p>
<p>Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.</p>
<p>Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.</p>https://thesis.library.caltech.edu/id/eprint/9549Electricity Markets for the Smart Grid: Networks, Timescales, and Integration with Control
https://resolver.caltech.edu/CaltechTHESIS:05262016-112813537
Authors: {'items': [{'email': 'desmond.cai@gmail.com', 'id': 'Cai-Wuhan-Desmond', 'name': {'family': 'Cai', 'given': 'Wuhan Desmond'}, 'orcid': '0000-0001-9207-1890', 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z9BG2KZG
<p>We are at the dawn of a significant transformation in the electric industry. Renewable generation and customer participation in grid operations and markets have been growing at tremendous rates in recent years and these trends are expected to continue. These trends are likely to be accompanied by both engineering and market integration challenges. Therefore, to incorporate these resources efficiently into the grid, it is important to deal with the inefficiencies in existing markets. The goal of this thesis is to contribute new insights towards improving the design of electricity markets.</p>
<p>This thesis makes three main contributions. First, we provide insights into how the economic dispatch mechanism could be designed to account for price-anticipating participants. We study this problem in the context of a networked Cournot competition with a market maker and we give an algorithm to find improved market clearing designs. Our findings illustrate the potential inefficiencies in existing markets and provides a framework for improving the design of the markets. Second, we provide insights into the strategic interactions between generation flexibility and forward markets. Our key insight is an observation that spot market capacity constraints can significantly impact the efficiency and existence of equilibrium in forward markets, as they give producers incentives to strategically withhold offers from the markets. Third, we provide insights into how optimization decomposition theory can guide optimal design of the architecture of power systems control. In particular, we illustrate a context where decomposition theory enables us to jointly design market and control mechanisms to allocate resources efficiently across both the economic dispatch and frequency regulation timescales.
</p>https://thesis.library.caltech.edu/id/eprint/9765Optimization and Control of Power Flow in Distribution Networks
https://resolver.caltech.edu/CaltechTHESIS:12092015-021431773
Authors: {'items': [{'email': 'mfarivar@gmail.com', 'id': 'Farivar-Masoud', 'name': {'family': 'Farivar', 'given': 'Masoud'}, 'orcid': '0000-0001-7298-3526', 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z9JW8BSM
<p>Climate change is arguably the most critical issue facing our generation and the next. As we move towards a sustainable future, the grid is rapidly evolving with the integration of more and more renewable energy resources and the emergence of electric vehicles. In particular, large scale adoption of residential and commercial solar photovoltaics (PV) plants is completely changing the traditional slowly-varying unidirectional power flow nature of distribution systems. High share of intermittent renewables pose several technical challenges, including voltage and frequency control. But along with these challenges, renewable generators also bring with them millions of new DC-AC inverter controllers each year. These fast power electronic devices can provide an unprecedented opportunity to increase energy efficiency and improve power quality, if combined with well-designed inverter control algorithms. The main goal of this dissertation is to develop scalable power flow optimization and control methods that achieve system-wide efficiency, reliability, and robustness for power distribution networks of future with high penetration of distributed inverter-based renewable generators.</p>
<p>Proposed solutions to power flow control problems in the literature range from fully centralized to fully local ones. In this thesis, we will focus on the two ends of this spectrum. In the first half of this thesis (chapters 2 and 3), we seek optimal solutions to voltage control problems provided a centralized architecture with complete information. These solutions are particularly important for better understanding the overall system behavior and can serve as a benchmark to compare the performance of other control methods against. To this end, we first propose a branch flow model (BFM) for the analysis and optimization of radial and meshed networks. This model leads to a new approach to solve optimal power flow (OPF) problems using a two step relaxation procedure, which has proven to be both reliable and computationally efficient in dealing with the non-convexity of power flow equations in radial and weakly-meshed distribution networks. We will then apply the results to fast time- scale inverter var control problem and evaluate the performance on real-world circuits in Southern California Edison’s service territory.</p>
<p>The second half (chapters 4 and 5), however, is dedicated to study local control approaches, as they are the only options available for immediate implementation on today’s distribution networks that lack sufficient monitoring and communication infrastructure. In particular, we will follow a reverse and forward engineering approach to study the recently proposed piecewise linear volt/var control curves. It is the aim of this dissertation to tackle some key problems in these two areas and contribute by providing rigorous theoretical basis for future work.</p>https://thesis.library.caltech.edu/id/eprint/9317Real-Time Load-Side Control of Electric Power Systems
https://resolver.caltech.edu/CaltechTHESIS:05232016-160307020
Authors: {'items': [{'email': 'zhchangh1987@gmail.com', 'id': 'Zhao-Changhong', 'name': {'family': 'Zhao', 'given': 'Changhong'}, 'orcid': '0000-0003-0539-8591', 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z9RN35TJ
<p>Two trends are emerging from modern electric power systems: the growth of renewable (e.g., solar and wind) generation, and the integration of information technologies and advanced power electronics. The former introduces large, rapid, and random fluctuations in power supply, demand, frequency, and voltage, which become a major challenge for real-time operation of power systems. The latter creates a tremendous number of controllable intelligent endpoints such as smart buildings and appliances, electric vehicles, energy storage devices, and power electronic devices that can sense, compute, communicate, and actuate. Most of these endpoints are distributed on the load side of power systems, in contrast to traditional control resources such as centralized bulk generators. This thesis focuses on controlling power systems in real time, using these load side resources. Specifically, it studies two problems.</p>
<p>(1) Distributed load-side frequency control: We establish a mathematical framework to design distributed frequency control algorithms for flexible electric loads. In this framework, we formulate a category of optimization problems, called optimal load control (OLC), to incorporate the goals of frequency control, such as balancing power supply and demand, restoring frequency to its nominal value, restoring inter-area power flows, etc., in a way that minimizes total disutility for the loads to participate in frequency control by deviating from their nominal power usage. By exploiting distributed algorithms to solve OLC and analyzing convergence of these algorithms, we design distributed load-side controllers and prove stability of closed-loop power systems governed by these controllers. This general framework is adapted and applied to different types of power systems described by different models, or to achieve different levels of control goals under different operation scenarios. We first consider a dynamically coherent power system which can be equivalently modeled with a single synchronous machine. We then extend our framework to a multi-machine power network, where we consider primary and secondary frequency controls, linear and nonlinear power flow models, and the interactions between generator dynamics and load control. </p>
<p>(2) Two-timescale voltage control: The voltage of a power distribution system must be maintained closely around its nominal value in real time, even in the presence of highly volatile power supply or demand. For this purpose, we jointly control two types of reactive power sources: a capacitor operating at a slow timescale, and a power electronic device, such as a smart inverter or a D-STATCOM, operating at a fast timescale. Their control actions are solved from optimal power flow problems at two timescales. Specifically, the slow-timescale problem is a chance-constrained optimization, which minimizes power loss and regulates the voltage at the current time instant while limiting the probability of future voltage violations due to stochastic changes in power supply or demand. This control framework forms the basis of an optimal sizing problem, which determines the installation capacities of the control devices by minimizing the sum of power loss and capital cost. We develop computationally efficient heuristics to solve the optimal sizing problem and implement real-time control. Numerical experiments show that the proposed sizing and control schemes significantly improve the reliability of voltage control with a moderate increase in cost.</p>https://thesis.library.caltech.edu/id/eprint/9739Optimal Sensor Placement for Bayesian Parametric Identification of Structures
https://resolver.caltech.edu/CaltechTHESIS:05182017-090742614
Authors: {'items': [{'email': 'pinaky.bhattacharyya@gmail.com', 'id': 'Bhattacharyya-Pinaky', 'name': {'family': 'Bhattacharyya', 'given': 'Pinaky'}, 'orcid': '0000-0003-3773-0392', 'show_email': 'YES'}]}
Year: 2017
DOI: 10.7907/Z9H41PG5
<p>There exists a choice in where to place sensors to collect data for Bayesian model updating and system identification of structures. It is desirable to use an available deterministic predictive model, such as a finite-element model, along with prior information on the uncertain model parameters and the uncertain accuracy of the predictive model, to determine which optimal sensor locations should be instrumented in the structure. In this thesis, an information-theoretic framework for optimality is considered.</p>
<p>The mutual information between the uncertain model predictions for the data and the uncertain model parameters is presented as a natural measure of reduction in uncertainty to maximize over sensor configurations. A combinatorial search over all sensor configurations is usually prohibitively expensive. A convex optimization method is developed to provide a fast sub-optimal, but possibly optimal, sensor configuration when certain simplifying assumptions can be made about the chosen stochastic model class for the structure. The optimization method is demonstrated to work for a 50-story uniform shear building, with 20 sensors to be installed.</p>
<p>The stability of optimal sensor configurations under refinement of the mesh of the underlying finite-element model is investigated and related to the choice of prediction-error correlations in the model. An example problem of placement of a single sensor on the continuum of an elastic axial bar is solved analytically.</p>
<p>In order to solve the optimal sensor placement problem in the more general case, numerical estimation of mutual information between the model predictions for the data and the model parameters becomes necessary. To this end, a thermodynamic integration scheme based on path sampling is developed with the aim of estimating the entropy of the data prediction distribution. The scheme is demonstrated to work for an example that uses synthetic data for model class comparison between linear and Duffing oscillator model classes. The thermodynamic integration method is then used to determine the optimal location of a single sensor for a two degree-of-freedom oscillator model.</p>
https://thesis.library.caltech.edu/id/eprint/10181A Study of Communication Networks through the Lens of Reduction
https://resolver.caltech.edu/CaltechTHESIS:06072017-154010713
Authors: {'items': [{'email': 'wongmingfai@gmail.com', 'id': 'Wong-Ming-Fai', 'name': {'family': 'Wong', 'given': 'Ming Fai'}, 'orcid': '0000-0002-9191-1277', 'show_email': 'YES'}]}
Year: 2017
DOI: 10.7907/Z9348HFK
<p>A central goal of information theory is to characterize the capacity regions of communication networks. Due to the difficulty of the general problem, research is primarily focused on families of problems defined by various classifiers. These classifiers include the channel transition function (i.e., noisy, deterministic, network coding), demand type (i.e., single-source, 2-unicast), network topology (i.e. acyclic network coding, index coding). To date, the families of networks that are fully solved remain limited. Moreover, results derived for one specific family often do not extend easily to other families of problems.</p>
<p>Our work shifts from the traditional focus on solving example networks to one that builds connections between problem solutions so that we can say where and when solving a problem in one domain would also solve a corresponding problem in another domain. Central to our approach is a technique called "reduction", in which we connect the solutions and results of communication problems. We say that problem A reduces to problem B when A can be solved by first transforming it to B and then applying a solution for B. We focus on two notions of reduction: reduction in code design and reduction in capacity region.</p>
<p>Our central results demonstrate reductions with respect to a variety of classifiers. We show that finding multiple multicast network capacity regions reduces to finding multiple unicast network capacity regions both when capacity is defined as the maximal rate over all possible codes and when capacity is defined as the optimal rate over linear codes. As a corollary to this result, we show that the same capacity reduction holds for when network types are limited to either network coding networks or index coding networks. In several instances, we show that a reduction in code design extends to a reduction in capacity region if and only if the edge removal conjecture holds. Here, the edge removal conjecture states that removing an edge of negligible capacity from a network does not change its capacity region.</p>
<p>One of the key challenges in network coding research is how to handle networks containing cycles. As a result, many papers on network coding restrict attention to acyclic networks and some results derived for acyclic networks do not extend to networks containing cycles. We consider a streaming model for network communication where information is streamed to its destination under a constraint on maximal delay at the decoder. Restricting our attention to this scenario enables us to prove a code reduction from network coding to index coding in both acyclic and cyclic networks. Since index coding networks are acyclic, a consequence of this reduction is that under the streaming model, there is no fundamental difference between acyclic and cyclic networks.</p>https://thesis.library.caltech.edu/id/eprint/10311Coding for Security and Reliability in Distributed Systems
https://resolver.caltech.edu/CaltechTHESIS:06042017-212503971
Authors: {'items': [{'email': 'yelohuang@gmail.com', 'id': 'Huang-Wentao', 'name': {'family': 'Huang', 'given': 'Wentao'}, 'orcid': '0000-0003-0963-3624', 'show_email': 'YES'}]}
Year: 2017
DOI: 10.7907/Z9P26W5C
<p>This dissertation studies the use of coding techniques to improve the reliability and security of distributed systems. The first three parts focus on distributed storage systems, and study schemes that encode a message into <i>n</i> shares, assigned to <i>n</i> nodes, such that any <i>n</i> - <i>r</i> nodes can decode the message (reliability) and any colluding <i>z</i> nodes cannot infer any information about the message (security). The objective is to optimize the computational, implementation, communication and access complexity of the schemes during the process of encoding, decoding and repair. These are the key metrics of the schemes so that when they are applied in practical distributed storage systems, the systems are not only reliable and secure, but also fast and cost-effective.</p>
<p>Schemes with highly efficient computation and implementation are studied in Part I. For the practical high rate case of <i>r</i> ≤ 3 and <i>z</i> ≤ 3, we construct schemes that require only <i>r</i> + <i>z</i> XORs to encode and <i>z</i> XORs to decode each message bit, based on practical erasure codes including the B, EVENODD and STAR codes. This encoding and decoding complexity is shown to be optimal. For general <i>r</i> and <i>z</i>, we design schemes over a special ring from Cauchy matrices and Vandermonde matrices. Both schemes can be efficiently encoded and decoded due to the structure of the ring. We also discuss methods to shorten the proposed schemes.</p>
<p>Part II studies schemes that are efficient in terms of communication and access complexity. We derive a lower bound on the decoding bandwidth, and design schemes achieving the optimal decoding bandwidth and access. We then design schemes that achieve the optimal bandwidth and access not only for decoding, but also for repair. Furthermore, we present a family of Shamir's schemes with asymptotically optimal decoding bandwidth.</p>
<p>Part III studies the problem of secure repair, i.e., reconstructing the share of a (failed) node without leaking any information about the message. We present generic secure repair protocols that can securely repair any linear schemes. We derive a lower bound on the secure repair bandwidth and show that the proposed protocols are essentially optimal in terms of bandwidth.</p>
<p>In the final part of the dissertation, we study the use of coding techniques to improve the reliability and security of network communication.</p>
<p>Specifically, in Part IV we draw connections between several important problems in network coding. We present reductions that map an arbitrary multiple-unicast network coding instance to a unicast secure network coding instance in which at most one link is eavesdropped, or a unicast network error correction instance in which at most one link is erroneous, such that a rate tuple is achievable in the multiple-unicast network coding instance if and only if a corresponding rate is achievable in the unicast secure network coding instance, or in the unicast network error correction instance. Conversely, we show that an arbitrary unicast secure network coding instance in which at most one link is eavesdropped can be reduced back to a multiple-unicast network coding instance. Additionally, we show that the capacity of a unicast network error correction instance in general is not (exactly) achievable. We derive upper bounds on the secrecy capacity for the secure network coding problem, based on cut-sets and the connectivity of links. Finally, we study optimal coding schemes for the network error correction problem, in the setting that the network and adversary parameters are not known a priori.</p>https://thesis.library.caltech.edu/id/eprint/10269Computational Methods for Bayesian Inference in Complex Systems
https://resolver.caltech.edu/CaltechTHESIS:06042017-011739366
Authors: {'items': [{'email': 'picatanach@gmail.com', 'id': 'Catanach-Thomas-Anthony', 'name': {'family': 'Catanach', 'given': 'Thomas Anthony'}, 'orcid': '0000-0002-4321-3159', 'show_email': 'NO'}]}
Year: 2017
DOI: 10.7907/Z9RX9948
<p>Bayesian methods are critical for the complete understanding of complex systems. In this approach, we capture all of our uncertainty about a system’s properties using a probability distribution and update this understanding as new information becomes available. By taking the Bayesian perspective, we are able to effectively incorporate our prior knowledge about a model and to rigorously assess the plausibility of candidate models based upon observed data from the system. We can then make probabilistic predictions that incorporate uncertainties, which allows for better decision making and design. However, while these Bayesian methods are critical, they are often computationally intensive, thus necessitating the development of new approaches and algorithms.</p>
<p>In this work, we discuss two approaches to Markov Chain Monte Carlo (MCMC). For many statistical inference and system identification problems, the development of MCMC made the Bayesian approach possible. However, as the size and complexity of inference problems has dramatically increased, improved MCMC methods are required. First, we present Second-Order Langevin MCMC (SOL-MC), a stochastic dynamical system-based MCMC algorithm that uses the damped second-order Langevin stochastic differential equation (SDE) to sample a desired posterior distribution. Since this method is based on an underlying dynamical system, we can utilize existing work in the theory for dynamical systems to develop, implement, and optimize the sampler's performance. Second, we present advances and theoretical results for Sequential Tempered MCMC (ST-MCMC) algorithms. Sequential Tempered MCMC is a family of parallelizable algorithms, based upon Transitional MCMC and Sequential Monte Carlo, that gradually transform a population of samples from the prior to the posterior through a series of intermediate distributions. Since the method is population-based, it can easily be parallelized. In this work, we derive theoretical results to help tune parameters within the algorithm. We also introduce a new sampling algorithm for ST-MCMC called the Rank-One Modified Metropolis Algorithm (ROMMA). This algorithm improves sampling efficiency for inference problems where the prior distribution constrains the posterior. In particular, this is shown to be relevant for problems in geophysics.</p>
<p>We also discuss the application of Bayesian methods to state estimation, disturbance detection, and system identification problems in complex systems. We introduce a Bayesian perspective on learning models and properties of physical systems based upon a layered architecture that can learn quickly and flexibly. We then apply this architecture to detecting and characterizing changes in physical systems with applications to power systems and biology. In power systems, we develop a new formulation of the Extended Kalman Filter for estimating dynamic states described by differential algebraic equations. This filter is then used as the basis for sub-second fault detection and classification. In synthetic biology, we use a Bayesian approach to detect and identify unknown chemical inputs in a biosensor system implemented in a cell population. This approach uses the tools of Bayesian model selection.</p>https://thesis.library.caltech.edu/id/eprint/10263Online Algorithms: From Prediction to Decision
https://resolver.caltech.edu/CaltechTHESIS:10182017-210853845
Authors: {'items': [{'email': 'niangjun@gmail.com', 'id': 'Chen-Niangjun', 'name': {'family': 'Chen', 'given': 'Niangjun'}, 'orcid': '0000-0002-2289-9737', 'show_email': 'YES'}]}
Year: 2018
DOI: 10.7907/Z95M63W4
<p>Making use of predictions is a crucial, but under-explored, area of sequential decision problems with limited information. While in practice most online algorithms rely on predictions to make real time decisions, in theory their performance is only analyzed in simplified models of prediction noise, either adversarial or i.i.d. The goal of this thesis is to bridge this divide between theory and practice: to study online algorithm under more practical predictions models, gain better understanding about the value of prediction, and design online algorithms that make the best use of predictions.</p>
<p>This thesis makes three main contributions. First, we propose a stochastic prediction error model that generalizes prior models in the learning and stochastic control communities, incorporates correlation among prediction errors, and captures the fact that predictions improve as time passes. Using this general prediction model, we prove that Averaging Fixed Horizon Control (AFHC) can simultaneously achieve sublinear regret and constant competitive ratio in expectation using only a constant- sized prediction window, overcoming the hardnesss results in adversarial prediction models. Second, to understand the optimal use of noisy prediction, we introduce a new class of policies, Committed Horizon Control (CHC), that generalizes both popular policies Receding Horizon Control (RHC) and Averaging Fixed Horizon Control (AFHC). Our results provide explicit results characterizing the optimal use of prediction in CHC policy as a function of properties of the prediction noise, e.g., variance and correlation structure. Third, we apply the general prediction model and algorithm design framework to the deferrable load control problem in power systems. Our proposed model predictive algorithm provides significant reduction in variance of total load in the power system. Throughout this thesis, we provide both average-case analysis and concentration results for our proposed online algorithms, highlighting that the typical performance is tightly concentrated around the average-case performance.</p>https://thesis.library.caltech.edu/id/eprint/10530Optimizing Resource Management in Cloud Analytics Services
https://resolver.caltech.edu/CaltechTHESIS:05312018-080301508
Authors: {'items': [{'email': 'xiaoqiren.viola@gmail.com', 'id': 'Ren-Xiaoqi', 'name': {'family': 'Ren', 'given': 'Xiaoqi'}, 'orcid': '0000-0002-1121-9046', 'show_email': 'NO'}]}
Year: 2018
DOI: 10.7907/K62Y-FV39
<p>The fundamental challenge in the cloud today is how to build and optimize machine learning and data analytical services. Machine learning and data analytical platforms are changing computing infrastructure from expensive private data centers to easily accessible online services. These services pack user requests as jobs and run them on thousands of machines in parallel in geo-distributed clusters. The scale and the complexity of emerging jobs lead to increasing challenges for the clusters at all levels, from power infrastructure to system architecture and corresponding software framework design.</p>
<p>These challenges come in many forms. Today's clusters are built on commodity hardware and hardware failures are unavoidable. Resource competition, network congestion, and mixed generations of hardware make the hardware environment complex and hard to model and predict. Such heterogeneity becomes a crucial roadblock for efficient parallelization on both the task level and job level. Another challenge comes from the increasing complexity of the applications. For example, machine learning services run jobs made up of multiple tasks with complex dependency structures. This complexity leads to difficulties in framework designs. The scale, especially when services span geo-distributed clusters, leads to another important hurdle for cluster design. Challenges also come from the power infrastructure. Power infrastructure is very expensive and accounts for more than 20% of the total costs to build a cluster. Power sharing optimization to maximize the facility utilization and smooth peak hour usages is another roadblock for cluster design.</p>
<p>In this thesis, we focus on solutions for these challenges at the task level, on the job level, with respect to the geo-distributed data cloud design and for power management in colocation data centers.</p>
<p>At the task level, a crucial hurdle to achieving predictable performance is stragglers, i.e., tasks that take significantly longer than expected to run. At this point, speculative execution has been widely adopted to mitigate the impact of stragglers in simple workloads. We apply straggler mitigation for approximation jobs for the first time. We present GRASS, which carefully uses speculation to mitigate the impact of stragglers in approximation jobs. GRASS's design is based on the analysis of a model we develop to capture the optimal speculation levels for approximation jobs. Evaluations with production workloads from Facebook and Microsoft Bing in an EC2 cluster of 200 nodes show that GRASS increases accuracy of deadline-bound jobs by 47% and speeds up error-bound jobs by 38%.</p>
<p>Moving from task level to job level, task level speculation mechanisms are designed and operated independently of job scheduling when, in fact, scheduling a speculative copy of a task has a direct impact on the resources available for other jobs. Thus, we present Hopper, a job-level speculation-aware scheduler that integrates the tradeoffs associated with speculation into job scheduling decisions based on a model generalized from the task-level speculation model. We implement both centralized and decentralized prototypes of the Hopper scheduler and show that 50% (66%) improvements over state-of-the-art centralized (decentralized) schedulers and speculation strategies can be achieved through the coordination of scheduling and speculation.</p>
<p>As computing resources move from local clusters to geo-distributed cloud services, we are expecting the same transformation for data storage. We study two crucial pieces of a geo-distributed data cloud system: data acquisition and data placement. Starting from developing the optimal algorithm for the case of a data cloud made up of a single data center, we propose a near-optimal, polynomial-time algorithm for a geo-distributed data cloud in general. We show, via a case study, that the resulting design, Datum, is near-optimal (within 1.6%) in practical settings.</p>
<p>Efficient power management is a fundamental challenge for data centers when providing reliable services. Power oversubscription in data centers is very common and may occasionally trigger an emergency when the aggregate power demand exceeds the capacity. We study power capping solutions for handling such emergencies in a colocation data center, where the operator supplies power to multiple tenants. We propose a novel market mechanism based on supply function bidding, called COOP, to financially incentivize and coordinate tenants' power reduction for minimizing total performance loss while satisfying multiple power capping constraints. We demonstrate that COOP is "win-win", increasing the operator's profit (through oversubscription) and reducing tenants' costs (through financial compensation for their power reduction during emergencies).</p>https://thesis.library.caltech.edu/id/eprint/10978Impact of Transmission Network Topology on Electrical Power Systems
https://resolver.caltech.edu/CaltechTHESIS:05312019-191005982
Authors: {'items': [{'email': 'linqi.guo.cms@gmail.com', 'id': 'Guo-Linqi', 'name': {'family': 'Guo', 'given': 'Linqi'}, 'orcid': '0000-0001-5771-2752', 'show_email': 'NO'}]}
Year: 2019
DOI: 10.7907/EN8K-W872
<p>Power system reliability is a crucial component in the development of sustainable infrastructure. Because of the intricate interactions among power system components, it is often difficult to make general inferences on how the transmission network topology impacts performance of the grid in different scenarios. This complexity poses significant challenges for researches in the modeling, control, and management of power systems.</p>
<p>In this work, we develop a theory that aims to address this challenge from both the fast-timescale and steady state aspects of power grids. Our analysis builds upon the transmission network Laplacian matrix, and reveals new properties of this well-studied concept in spectral graph theory that are specifically tailored to the power system context. A common theme of this work is the representation of certain physical quantities in terms of graphical structures, which allows us to establish algebraic results on power grid performance using purely topological information. This view is particularly powerful and often leads to surprisingly simple characterizations of complicated system behaviors. Depending on the timescale of the underlying problem, our results can be roughly categorized into the study of frequency regulation and the study of cascading failures.</p>
<p><i>Fast-timescale: Frequency Regulation</i>. We first study how the transmission network impacts power system robustness against disturbances in transient phase. Towards this goal, we develop a framework based on the Laplacian spectrum that captures the interplay among network topology, system inertia, and generator/load damping. This framework shows that the impact of network topology in frequency regulation can be quantified through the network Laplacian eigenvalues, and that such eigenvalues fully determine the grid robustness against low frequency perturbations. Moreover, we can explicitly decompose the frequency signal along scaled Laplacian eigenvectors when damping-inertia ratios are uniform across the buses. The insights revealed by this framework explain why load-side participation in frequency regulation not only makes the system respond faster, but also helps lower the system nadir after a disturbance, providing useful guidelines in the controller design. We simulate an improved controller reverse engineered from our results on the IEEE 39-bus New England interconnection system, and illustrate its robustness against high frequency oscillations compared to both the conventional droop control and a recent controller design.</p>
<p>We then switch to a more combinatorial problem that seeks to characterize the controllability and observability of the power system in frequency regulation if only a subset of buses are equipped with controllers/sensors. Our results show that the controllability/observability of the system depends on two orthogonal conditions: (a) intrinsic structure of the system graph, and (b) algebraic coverage of buses with controllers/sensors. Condition (a) encodes information on graph symmetry and is shown to hold for almost all practical systems. Condition (b) captures how buses interact with each other through the network and can be verified using the eigenvectors of the graph Laplacian matrix. Based on this characterization, the optimal placement of controllers and sensors in the network can be formulated as a set cover problem. We demonstrate how our results identify the critical buses in real systems using a simulation in the IEEE 39-bus New England interconnection test system. In particular, for this testbed a single well chosen bus is capable of providing full controllability and observability.</p>
<p><i>Steady State: Cascading Failures</i>. Cascading failures in power systems exhibit non-monotonic, non-local propagation patterns which make the analysis and mitigation of failures difficult. By studying the transmission network Laplacian matrix, we reveal two useful structures that make the analysis of this complex evolution more tractable: (a) In contrast to the lack of monotonicity in the physical system, there is a rich collection of monotonicity we can explore in the spectrum of the Laplacian matrix. This allows us to systematically design topological measures that are monotonic over the cascading event. (b) Power redistribution patterns are closely related to the distribution of different types of trees in the power network topology. Such graphical interpretation captures the Kirchhoff's Law in a precise way and naturally suggests that we can eliminate long-distance propagation of system disturbances by forming a tree-partition.</p>
<p>We then show that the tree-partition of transmission networks provides a precise analytical characterization of line failure localizability. Specifically, when a non-bridge line is tripped, the impact of this failure only propagates within well-defined components, which we refer to as cells, of the tree-partition defined by the bridges. In contrast, when a bridge line is tripped, the impact of this failure propagates globally across the network, affecting the power flow on all remaining transmission lines. This characterization suggests that it is possible to improve the system robustness by switching off certain transmission lines, so as to create more, smaller components in the tree-partition; thus spatially localizing line failures and making the grid less vulnerable to large-scale outages. We illustrate this approach using the IEEE 118-bus test system and demonstrate that switching off a negligible portion of transmission lines allows the impact of line failures to be significantly more localized without substantial changes in line congestion.</p>
<p><i>Unified Controller on Tree-partitions</i>. Combining our results from both the fast-timescale and steady state behaviors of power grids, we propose a distributed control strategy that offers strong guarantees in both the mitigation and localization of cascading failures in power systems. This control strategy leverages a new controller design known as Unified Controller (UC) from frequency regulation literature, and revolves around the powerful properties that emerge when the management areas that UC operates over form a tree-partition. After an initial failure, the proposed strategy always prevents successive failures from happening, and regulates the system to the desired steady state where the impact of initial failures are localized as much as possible. For extreme failures that cannot be localized, the proposed framework has a configurable design that progressively involves and coordinates across more control areas for failure mitigation and, as a last resort, imposes minimal load shedding. We compare the proposed control framework with the classical Automatic Generation Control (AGC) on the IEEE 118-bus test system. Simulation results show that our novel control greatly improves the system robustness in terms of the <i>N-1</i> security standard, and localizes the impact of initial failures in majority of the load profiles that are examined. Moreover, the proposed framework incurs significantly less load loss, if any, compared to AGC, in all of our case studies.</p>https://thesis.library.caltech.edu/id/eprint/11590Time-Varying Optimization and Its Application to Power System Operation
https://resolver.caltech.edu/CaltechTHESIS:01222019-221628111
Authors: {'items': [{'email': 'tyj518@gmail.com', 'id': 'Tang-Yujie', 'name': {'family': 'Tang', 'given': 'Yujie'}, 'orcid': '0000-0002-4921-8372', 'show_email': 'YES'}]}
Year: 2019
DOI: 10.7907/6N9W-3J20
The main topic of this thesis is time-varying optimization, which studies algorithms that can track optimal trajectories of optimization problems that evolve with time. A typical time-varying optimization algorithm is implemented in a running fashion in the sense that the underlying optimization problem is updated during the iterations of the algorithm, and is especially suitable for optimizing large-scale fast varying systems. Motivated by applications in power system operation, we propose and analyze first-order and second-order running algorithms for time-varying nonconvex optimization problems.
The first-order algorithm we propose is the regularized proximal primal-dual gradient algorithm, and we develop a comprehensive theory on its tracking performance. Specifically, we provide analytical results in terms of tracking a KKT point, and derive bounds for the tracking error defined as the distance between the algorithmic iterates and a KKT trajectory. We then provide sufficient conditions under which there exists a set of algorithmic parameters that guarantee that the tracking error bound holds. Qualitatively, the sufficient conditions for the existence of feasible parameters suggest that the problem should be "sufficiently convex" around a KKT trajectory to overcome the nonlinearity of the nonconvex constraints. The study of feasible algorithmic parameters motivates us to analyze the continuous-time limit of the discrete-time algorithm, which we formulate as a system of differential inclusions; results on its tracking performance as well as feasible and optimal algorithmic parameters are also derived. Finally, we derive conditions under which the KKT points for a given time instant will always be isolated so that bifurcations or merging of KKT trajectories do not happen.
The second-order algorithms we develop are approximate Newton methods that incorporate second-order information. We first propose the approximate Newton method for a special case where there are no explicit inequality or equality constraints. It is shown that good estimation of second-order information is important for achieving satisfactory tracking performance. We also propose a specific version of the approximate Newton method based on L-BFGS-B that handles box constraints. Then, we propose two variants of the approximate Newton method that handle explicit inequality and equality constraints. The first variant employs penalty functions to obtain a modified version of the original problem, so that the approximate Newton method for the special case can be applied. The second variant can be viewed as an extension of the sequential quadratic program in the time-varying setting.
Finally, we discuss application of the proposed algorithms to power system operation. We formulate the time-varying optimal power flow problem, and introduce partition of the decision variables that enables us to model the power system by an implicit power flow map. The implicit power flow map allows us to incorporate real-time feedback measurements naturally in the algorithm. The use of real-time feedback measurement is a central idea in real-time optimal power flow algorithms, as it helps reduce the computation burden and potentially improve robustness against model mismatch. We then present in detail two real-time optimal power flow algorithms, one based on the regularized proximal primal-dual gradient algorithm, and the other based on the approximate Newton method with the penalty approach.https://thesis.library.caltech.edu/id/eprint/11358Online Platforms in Networked Markets: Transparency, Anticipation and Demand Management
https://resolver.caltech.edu/CaltechTHESIS:03132019-143428796
Authors: {'items': [{'email': 'johnpzf@gmail.com', 'id': 'Pang-John-Zhen-Fu', 'name': {'family': 'Pang', 'given': 'John Zhen Fu'}, 'orcid': '0000-0002-6485-7922', 'show_email': 'YES'}]}
Year: 2019
DOI: 10.7907/XY8M-8D94
<p>The global economy has been transformed by the introduction of online platforms in the past two decades. These companies, such as Uber and Amazon, have benefited and undergone massive growth, and are a critical part of the world economy today. Understanding these online platforms, their designs and how participation change with anticipation and uncertainty can help us identify the necessary ingredients for successful implementation of online platforms in the future, especially for those with underlying network constraints, e.g., the electricity grid.</p>
<p>This thesis makes three main contributions. First, we identify and compare common access and allocation control designs for online platforms, and highlight their trade-offs between transparency and control. We make these comparisons under a networked Cournot competition model and consider three popular designs: (i) open access, (ii) discriminatory access, and (iii) controlled allocation. Our findings reveal that designs that control over access are more efficient than designs that control over allocations, but open access designs are susceptible to substantial search costs. Next, we study the impact of demand management in a networked Stackelberg model considering network constraints and producer anticipation. We provide insights on limiting manipulation under these constrained networked marketplaces with nodal prices, and show that demand management mechanisms that traditionally aid system stability also help plays a vital role economically. In particular, we show that demand management empower consumers and give them "market power" to counter that of producers, limiting the impact of their anticipation and their potential for manipulation. Lastly, we study how participants (e.g., drivers on Uber) make competitive real-time production (driving) decisions. To that end, we design a novel pursuit algorithm for making online optimization under limited inventory constraints. Our analysis yields an algorithm that is competitive and applicable to achieve optimal results in the well known one-way trading problem, and new variants of the original problem.</p>https://thesis.library.caltech.edu/id/eprint/11425Convex Relaxations for Graph and Inverse Eigenvalue Problems
https://resolver.caltech.edu/CaltechTHESIS:01152020-210801253
Authors: {'items': [{'email': 'utkancandogan@gmail.com', 'id': 'Candogan-Utkan-Onur', 'name': {'family': 'Candogan', 'given': 'Utkan Onur'}, 'orcid': '0000-0002-1416-4909', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/ZV0D-SW58
<p>This thesis is concerned with presenting convex optimization based tractable solutions for three fundamental problems:</p>
<p>1. <i>Planted subgraph problem</i>: Given two graphs, identifying the subset of vertices of the larger graph corresponding to the smaller one.</p>
<p>2. <i>Graph edit distance problem</i>: Given two graphs, calculating the number of edge/vertex additions and deletions required to transform one graph into the other.</p>
<p>3. <i>Affine inverse eigenvalue problem</i>: Given a subspace <b>ε</b> ⊂ 𝕊ⁿ and a vector of eigenvalues λ ∈ ℝⁿ, finding a symmetric matrix with spectrum λ contained in <b>ε</b>.</p>
<p>These combinatorial and algebraic problems frequently arise in various application domains such as social networks, computational biology, chemoinformatics, and control theory. Nevertheless, exactly solving them in practice is only possible for very small instances due to their complexity. For each of these problems, we introduce convex relaxations which succeed in providing exact or approximate solutions in a computationally tractable manner.</p>
<p>Our relaxations for the two graph problems are based on convex graph invariants, which are functions of graphs that do not depend on a particular labeling. One of these convex relaxations, coined the Schur-Horn orbitope, corresponds to the convex hull of all matrices with a given spectrum, and plays a prominent role in this thesis. Specifically, we utilize relaxations based on the Schur-Horn orbitope in the context of the planted subgraph problem and the graph edit distance problem. For both of these problems, we identify conditions under which the Schur-Horn orbitope based relaxations exactly solve the corresponding problem with overwhelming probability. Specifically, we demonstrate that these relaxations turn out to be particularly effective when the underlying graph has a spectrum comprised of few distinct eigenvalues with high multiplicities. In addition to relaxations based on the Schur-Horn orbitope, we also consider outer-approximations based on other convex graph invariants such as the stability number and the maximum-cut value for the graph edit distance problem. On the other hand, for the inverse eigenvalue problem, we investigate two relaxations arising from a sum of squares hierarchy. These relaxations have different approximation qualities, and accordingly induce different computational costs. We utilize our framework to generate solutions for, or certify unsolvability of the underlying inverse eigenvalue problem.</p>
<p>We particularly emphasize the computational aspect of our relaxations throughout this thesis. We corroborate the utility of our methods with various numerical experiments.</p>https://thesis.library.caltech.edu/id/eprint/13622Applications of Convex Analysis to Signomial and Polynomial Nonnegativity Problems
https://resolver.caltech.edu/CaltechTHESIS:05202021-194439071
Authors: {'items': [{'email': 'rjmurray201693@gmail.com', 'id': 'Murray-Riley-John', 'name': {'family': 'Murray', 'given': 'Riley John'}, 'orcid': '0000-0003-1461-6458', 'show_email': 'NO'}]}
Year: 2021
DOI: 10.7907/vn9x-xj10
<p>Here is a question that is easy to state, but often hard to answer:</p>
<p><i>Is this function nonnegative on this set?</i></p>
<p>When faced with such a question, one often makes appeals to known inequalities. One crafts arguments that are <i>sufficient</i> to establish the nonnegativity of the function, rather than determining the function's precise range of values. This thesis studies sufficient conditions for nonnegativity of signomials and polynomials. Conceptually, signomials may be viewed as generalized polynomials that feature arbitrary real exponents, but with variables restricted to the positive orthant.</p>
<p>Our methods leverage efficient algorithms for a type of convex optimization known as relative entropy programming (REP). By virtue of this integration with REP, our methods can help answer questions like the following:</p>
<p>Is there some function, in this particular space of functions, that is nonnegative on this set?</p>
<p>The ability to answer such questions is <i>extremely</i> useful in applied mathematics.
Alternative approaches in this same vein (e.g., methods for polynomials based on semidefinite programming)
have been used successfully as convex relaxation frameworks for nonconvex optimization, as mechanisms for analyzing dynamical systems, and even as tools for solving nonlinear partial differential equations.</p>
<p>This thesis builds from the <i>sums of arithmetic-geometric exponentials</i> or <i>SAGE</i> approach to signomial nonnegativity. The term "exponential" appears in the SAGE acronym because SAGE parameterizes signomials in terms of exponential functions.</p>
<p>Our first round of contributions concern the original SAGE approach. We employ basic techniques in convex analysis and convex geometry to derive structural results for spaces of SAGE signomials and exactness results for SAGE-based REP relaxations of nonconvex signomial optimization problems.
We frame our analysis primarily in terms of the coefficients of a signomial's basis expansion rather than in terms of signomials themselves.
The effect of this framing is that our results for signomials readily transfer to polynomials. In particular, we are led to define a new concept of <i>SAGE polynomials</i>. For sparse polynomials, this method offers an exponential efficiency improvement relative to certificates of nonnegativity obtained through semidefinite programming.</p>
<p>We go on to create the <i>conditional SAGE</i> methodology for exploiting convex substructure in constrained signomial nonnegativity problems.
The basic insight here is that since the standard relative entropy representation of SAGE signomials is obtained by a suitable application of convex duality, we are free to add additional convex constraints into the duality argument. In the course of explaining this idea we provide some illustrative examples in signomial optimization and analysis of chemical dynamics.</p>
<p>The majority of this thesis is dedicated to exploring fundamental questions surrounding conditional SAGE signomials. We approach these questions through analysis frameworks of <i>sublinear circuits</i> and <i>signomial rings</i>. These sublinear circuits generalize simplicial circuits of affine-linear matroids, and lead to rich modes of analysis for sets that are simultaneously convex in the usual sense and convex under a logarithmic transformation. The concept of signomial rings lets us develop a powerful signomial Positivstellensatz and an elementary signomial moment theory. The Positivstellensatz provides for an effective hierarchy of REP relaxations for approaching the value of a nonconvex signomial minimization problem from below, as well as a first-of-its-kind hierarchy for approaching the same value from above.</p>
<p>In parallel with our mathematical work, we have developed the sageopt python package. Sageopt drives all the examples and experiments used throughout this thesis, and has been used by engineers to solve high-degree polynomial optimization problems at scales unattainable by alternative methods.
We conclude this thesis with an explanation of how our theoretical results affected sageopt's design.</p>https://thesis.library.caltech.edu/id/eprint/14169Optimizing Cloud AI Platforms: Resource Allocation and Market Design
https://resolver.caltech.edu/CaltechTHESIS:06072021-172842077
Authors: {'items': [{'email': 'suyu2015@gmail.com', 'id': 'Su-Yu', 'name': {'family': 'Su', 'given': 'Yu'}, 'orcid': '0000-0002-7159-4542', 'show_email': 'NO'}]}
Year: 2021
DOI: 10.7907/bc2t-er54
<p>The numerous applications of data-driven algorithms and tools across diverse industries have led to tremendous successes in recent years. As the volume of massive data that is created, collected, and consumed continues to grow, there are many new imposed challenges faced by today's cloud AI platforms that support the deployment of machine learning algorithms on a large scale. In this thesis, we tackle the emerging challenges within cloud AI systems and beyond by adopting approaches from the fields of resource allocation and market design.</p>
<p>First, we propose a new scheduler, Generalized Earliest Time First (GETF), and provide the provable, worst-case approximation guarantees for the goals of minimizing both makespan and total weighted completion time of tasks with precedence constraints on related machines with machine-dependent communication times. These two results address long-standing open problems. Further, we adopt the classic speed scaling function to model power consumption and use mean response time to measure the performance. We propose the concept of pseudo-size to quantify importance of tasks and design a family of two-stage scheduling frameworks based on the approximation of pseudo-size. Assuming a good approximation of pseudo-size, we are able to provide the first provable bound of a linear combination of performance and energy goals under this setting.</p>
<p>Second, we study the design of mechanisms for data acquisition in settings with information leakage and verifiable data. We provide the first characterization of an optimal mechanism for data acquisition if agents are concerned about privacy and their data is correlated with each other. Additionally, the mechanism allows, for the first time, a trade-off between the bias and variance of the estimator. Transitioning from the data market into the energy market, we propose a new pricing scheme, which is applicable to general non-convex costs, and allows using general parametric pricing functions. Optimizing for the quantities and the price parameters simultaneously, and the ability to use general parametric pricing functions allows our scheme to find prices that are typically economically more efficient and less discriminatory than those of the existing schemes while still supporting a competitive equilibrium. In addition, we supplement the proposed method with a computationally efficient polynomial-time approximation algorithm, which can be used to approximate the optimal quantities and prices for general non-convex cost functions.</p>https://thesis.library.caltech.edu/id/eprint/14254Frameworks for High Dimensional Convex Optimization
https://resolver.caltech.edu/CaltechTHESIS:08162020-233437139
Authors: {'items': [{'email': 'londonpalma@gmail.com', 'id': 'London-Palma-Alise-den-Nijs', 'name': {'family': 'London', 'given': 'Palma Alise den Nijs'}, 'orcid': '0000-0001-6472-8293', 'show_email': 'NO'}]}
Year: 2021
DOI: 10.7907/db29-am33
<p>We present novel, efficient algorithms for solving extremely large optimization problems. A significant bottleneck today is that as the size of datasets grow, researchers across disciplines desire to solve prohibitively massive optimization problems. In this thesis, we present methods to compress optimization problems. The general goal is to represent a huge problem as a smaller problem or set of smaller problems, while still retaining enough information to ensure provable guarantees on solution quality and run time. We apply this approach to the following three settings.</p>
<p>First, we propose a framework for accelerating both linear program solvers and convex solvers for problems with linear constraints. Our focus is on a class of problems for which data is either very costly, or hard to obtain. In these situations, the number of data points m available is much smaller than the number of variables, n. In a machine learning setting, this regime is increasingly prevalent since it is often advantageous to consider larger and larger feature spaces, while not necessarily obtaining proportionally more data. Analytically, we provide worst-case guarantees on both the runtime and the quality of the solution produced. Empirically, we show that our framework speeds up state-of-the-art commercial solvers by two orders of magnitude, while maintaining a near-optimal solution.</p>
<p>Second, we propose a novel approach for distributed optimization which uses far fewer messages than existing methods. We consider a setting in which the problem data are distributed over the nodes. We provide worst-case guarantees on the performance with respect to the amount of communication it requires and the quality of the solution. The algorithm uses O(log(n+m)) messages with high probability. We note that this is an exponential reduction compared to the O(n) communication required during each round of traditional consensus based approaches. In terms of solution quality, our algorithm produces a feasible, near optimal solution. Numeric results demonstrate that the approximation error matches that of ADMM in many cases, while using orders-of-magnitude less communication.</p>
<p>Lastly, we propose and analyze a provably accurate long-step infeasible Interior Point Algorithm (IPM) for linear programming. The core computational bottleneck in IPMs is the need to solve a linear system of equations at each iteration. We employ sketching techniques to make the linear system computation lighter, by handling well-known ill-conditioning problems that occur when using iterative solvers in IPMs for LPs. In particular, we propose a preconditioned Conjugate Gradient iterative solver for the linear system. Our sketching strategy makes the condition number of the preconditioned system provably small. In practice we demonstrate that our approach significantly reduces the condition number of the linear system, and thus allows for more efficient solving on a range of benchmark datasets.</p>
https://thesis.library.caltech.edu/id/eprint/13856The Adaptive Charging Network Research Portal: Systems, Tools, and Algorithms
https://resolver.caltech.edu/CaltechTHESIS:05282021-174411678
Authors: {'items': [{'email': 'zach401@gmail.com', 'id': 'Lee-Zachary-Jordan', 'name': {'family': 'Lee', 'given': 'Zachary Jordan'}, 'orcid': '0000-0002-5358-2388', 'show_email': 'NO'}]}
Year: 2021
DOI: 10.7907/8eqg-e110
<p>Millions of electric vehicles (EVs) will enter service in the next decade, generating gigawatt-hours of additional energy demand. Charging these EVs cleanly, affordably, and without excessive stress on the grid will require advances in charging system design, hardware, monitoring, and control. Collectively, we refer to these advances as smart charging. While researchers have explored smart charging for over a decade, very few smart charging systems have been deployed in practice, leaving a sizeable gap between the research literature and the real world. In particular, we find that research is often based on simplified theoretical models. These simple models make analysis tractable but do not account for the complexities of physical systems. Moreover, researchers often lack the data needed to evaluate the performance of their algorithms on real workloads or apply techniques like machine learning. Even when promising algorithms are developed, they are rarely deployed since field tests can be costly and time-consuming.</p>
<p>The goal of this thesis is to develop systems, tools, and algorithms to bridge these gaps between theory and practice.</p>
<p>First, we describe the architecture of a first-of-its-kind smart charging system we call the Adaptive Charging Network (ACN).
Next, we use data and models from the ACN to develop a suite of tools to help researchers. These tools include ACN-Data, a public dataset of over 80,000 charging sessions; ACN-Sim, an open-source simulator based on realistic models; and ACN-Live, a platform for field testing algorithms on the ACN. Finally, we describe the algorithms we have developed using these tools. For example, we propose a practical and robust algorithm based on model predictive control, which can reduce infrastructure requirements by over 75%, increase operator profits by up to 3.4 times, and significantly reduce strain on the electric power grid. Other examples include a pricing scheme that fairly allocates costs to users considering time-of-use tariffs and demand charges and a data-driven approach to optimally size on-site solar generation with smart EV charging systems.</p>https://thesis.library.caltech.edu/id/eprint/14191Cascading Failures in Power Systems: Modeling, Characterization, and Mitigation
https://resolver.caltech.edu/CaltechTHESIS:06032022-035416994
Authors: {'items': [{'email': 'liangch93@gmail.com', 'id': 'Liang-Chen', 'name': {'family': 'Liang', 'given': 'Chen'}, 'orcid': '0000-0002-0015-7206', 'show_email': 'YES'}]}
Year: 2022
DOI: 10.7907/8817-xy25
<p>Reliability is a critical goal for power systems. Due to the connectivity of power grids, an initial failure may trigger a cascade of failures and eventually lead to a large-scale blackout, causing significant economic and social impacts. Cascading failure analysis thus draws wide attention from power system practitioners and researchers. A well-known observation is that cascading failures in power systems propagate non-locally because of the complex mechanism of power grids. Such non-local propagation makes it particularly challenging to model, analyze and control the failure process. In this thesis, we tackle these challenges by establishing a mathematical theory to model and characterize failure patterns, discover structural properties of failure propagation, and design novel techniques for failure mitigation.</p>
<p>First, we propose a failure propagation model considering both fast-timescale system frequency dynamics and the slow-timescale line tripping process. This model provides mathematical justifications to the widely used static DC model and can be generalized to capture a variety of failure propagation patterns induced by different control mechanisms of the power grid. More importantly, this model provides flexibility to design real-time control algorithms for failure mitigation and localization.</p>
<p>Second, we provide a complete characterization of line failures under the static DC model. Our results unveil a deep connection between the power redistribution patterns and the network block decomposition. More specifically, we show that a non-cut line failure in a block will only impact the branch power flows on the transmission lines within the block. In contrast, a cut set line failure will propagate globally depending on both the power balancing rules and the network topological structure. Further, we discuss three types of interface networks to connect the sub-grids, all achieving better failure localization performance.</p>
<p>Third, we study corrective control algorithms for failure mitigation. We integrate a distributed frequency control strategy with the network block decomposition to provide provable failure mitigation and localization guarantees on line failures. This strategy operates on the frequency control timescale and supplements existing corrective mechanisms, improving grid reliability and operational efficiency. We further explore the failure mitigation approach with direct post-contingency injection adjustments. Specifically, we propose an optimization-based control method with strong structural properties, which is highly desirable in large-scale power networks.</p>https://thesis.library.caltech.edu/id/eprint/14939Optimization of Distribution Power Networks: from Single-Phase to Multi-Phase
https://resolver.caltech.edu/CaltechTHESIS:06012022-005449566
Authors: {'items': [{'email': 'fengyuzhou1994@gmail.com', 'id': 'Zhou-Fengyu', 'name': {'family': 'Zhou', 'given': 'Fengyu'}, 'orcid': '0000-0002-2639-6491', 'show_email': 'NO'}]}
Year: 2022
DOI: 10.7907/tg26-9857
<p>Distributed energy resources play an important role in today's distribution power system. The Optimal Power Flow (OPF) problem is fundamental in power systems as many important applications such as economic dispatch, battery displacement, unit commitment, and voltage control can be formulated as an OPF. A paradoxical observation is the problem's complexity in theory but simplicity in practice. On the one hand, the problem is well known to be non-convex and NP-hard, so it is likely that no simple algorithms can solve all problem instances efficiently. On the other hand, there are many known algorithms which perform extremely well in practice for both standard test cases and real-world systems. This thesis attempts to reconcile this seeming contradiction.</p>
<p>Specifically, this thesis focuses on two types of properties that may underlie the simplicity in practice of OPF problems. The first property is the exactness of relaxations, meaning that one can find a convex relaxation of the original non-convex problem such that the two problems share the same optimal solution. This property would allow us to convexify the non-convex problem without altering the optimal solution and cost. The second property is that all locally optimal solutions of the non-convex problem are also globally optimal. This property allows us to apply local algorithms such as gradient descent without being trapped at some spurious local optima. We focus on distribution systems with radial networks (i.e., the underlying graphs are trees). We consider both single-phase models and unbalanced multi-phase models, since most real-world distribution systems are multi-phase unbalanced, and distributed energy resources (DERs) can be connected in either Wye or Delta configurations.</p>
<p>The main results of this thesis are two-fold. In the first half, we propose a class of sufficient conditions for a non-convex problem to simultaneously have exact relaxation and no spurious local optima. Then we apply the result to single-phase system and conclude that if all buses have no injection lowerbounds, then both properties (exactness and global optimality) can be achieved. While the same condition is already known to be sufficient for exactness, our work is the first to extend it to global optimality. In the second half, we focus on the exactness property for multi-phase systems. For systems without Delta connections, the exactness can be guaranteed if 1) the binding constraints are sparse in the network at optimality; or 2) all nodal prices fall within a narrow range. Using the DC model as an approximation, we further analyze the OPF sensitivity and explain why nodal prices tend to be close to each other. In the presence of Delta connections, we conclude that the inexactness can be resolved by either postprocessing an optimal solution, or adding a new regularization term in the cost function. Both methods achieve global optimality for IEEE standard test cases.</p>https://thesis.library.caltech.edu/id/eprint/14656Learning-Augmented Control and Decision-Making: Theory and Applications in Smart Grids
https://resolver.caltech.edu/CaltechThesis:07202022-040725024
Authors: {'items': [{'email': 'tongxinli@outlook.com', 'id': 'Li-Tongxin', 'name': {'family': 'Li', 'given': 'Tongxin'}, 'orcid': '0000-0002-9806-8964', 'show_email': 'NO'}]}
Year: 2023
DOI: 10.7907/cdf6-0w78
<p>Achieving carbon neutrality by 2050 does not only lead to the increasing penetration of renewable energy, but also an explosive growth of smart meter data. Recently, augmenting classical methods in real-world cyber-physical systems such as smart grids with black-box AI tools, forecasts, and ML algorithms has attracted a lot of growing interest. Integrating AI techniques into smart grids, on the one hand, provides a new approach to handle the uncertainties caused by renewable resources and human behaviors, but on the other hand, creates practical issues such as reliability, stability, privacy, and scalability, etc. to the AI-integrated algorithms.</p>
<p><em>This dissertation focuses on solving problems raised in designing learning-augmented control and decision-making algorithms.</em></p>
<p>The results presented in this dissertation are three-fold. We first study a problem in linear quadratic control, where imperfect/untrusted AI predictions of system perturbations are available. We show that it is possible to design a learning-augmented algorithm with performance guarantees that is aggressive if the predictions are accurate and conservative if they are imperfect. Machine-learned black-box policies are ubiquitous for nonlinear control problems. Meanwhile, crude model information is often available for these problems from, e.g., linear approximations of nonlinear dynamics. We next study the problem of equipping a black-box control policy with model-based advice for nonlinear control on a single trajectory. We first show a general negative result that a naive convex combination of a black-box policy and a linear model-based policy can lead to instability, even if the two policies are both stabilizing. We then propose an <em>adaptive λ-confident policy</em>, with a coefficient λ indicating the confidence in a black-box policy, and prove its stability. With bounded nonlinearity, in addition, we show that the adaptive λ-confident policy achieves a bounded competitive ratio when a black-box policy is near-optimal. Finally, we propose an online learning approach to implement the adaptive λ-confident policy and verify its efficacy in case studies about the Cart-Pole problem and a real-world electric vehicle (EV) charging problem with data bias due to COVID-19.</p>
<p>Aggregators have emerged as crucial tools for the coordination of distributed, controllable loads. To be used effectively, an aggregator must be able to communicate the available flexibility of the loads they control, known as the aggregate flexibility to a system operator. However, most existing aggregate flexibility measures often are slow-timescale estimations and much less attention has been paid to real-time coordination between an aggregator and an operator. In the second part of this dissertation, we consider solving an online decision-making problem in a closed-loop system and present a design of <em>real-time</em> aggregate flexibility feedback, termed the <em>maximum entropy feedback</em> (MEF). In addition to deriving analytic properties of the MEF, combining learning and control, we show that it can be approximated using reinforcement learning and used as a penalty term in a novel control algorithm--the <em>penalized predictive control</em> (PPC) that enables efficient communication, fast computation, and lower costs. We illustrate the efficacy of the PPC using a dataset from an adaptive electric vehicle charging network and show that PPC outperforms classical MPC. We show that under certain regularity assumptions, the PPC is optimal. We illustrate the efficacy of the PPC using a dataset from an adaptive electric vehicle charging network and show that PPC outperforms classical model predictive control (MPC). In a theoretical perspective, a two-controller problem is formulated. A central controller chooses an action from a feasible set that is determined by time-varying and coupling constraints, which depend on all past actions and states. The central controller's goal is to minimize the cumulative cost; however, the controller has access to neither the feasible set nor the dynamics directly, which are determined by a remote local controller. Instead, the central controller receives only an aggregate summary of the feasibility information from the local controller, which does not know the system costs. We show that it is possible for an online algorithm using feasibility information to nearly match the dynamic regret of an online algorithm using perfect information whenever the feasible sets satisfy some criterion, which is satisfied by inventory and tracking constraints.</p>
<p>The third part of this dissertation consists of examples of learning, inference, and data analysis methods for power system identification and electric charging. We present a power system identification problem with noisy nodal measurements and efficient algorithms, based on fundamental trade-offs between the number of measurements, the complexity of the graph class, and the probability of error. Next, we specifically consider prediction and unsupervised learning tasks in EV charging. We provide basic data analysis results of a public dataset released by Caltech and develop a novel iterative clustering method for classifying time series of EV charging rates.</p>https://thesis.library.caltech.edu/id/eprint/14980Uncertainty and Decentralization: Two Themes in an Energy Transformation
https://resolver.caltech.edu/CaltechTHESIS:06122023-232029846
Authors: {'items': [{'email': 'lucien.werner@gmail.com', 'id': 'Werner-Lucien-Desloge', 'name': {'family': 'Werner', 'given': 'Lucien Desloge'}, 'orcid': '0000-0003-1613-1702', 'show_email': 'NO'}]}
Year: 2023
DOI: 10.7907/scmm-p028
<p>Over the last two decades, the rapidly decreasing units costs of solar, wind, and energy storage technologies have launched a fundamental transformation in how electric power is produced, distributed, and consumed. Proliferation of these technologies has effected a shift towards a more decentralized, flexible, and sustainable energy system that can meet the growing demand for energy while reducing greenhouse gas emissions from fossil fuels. The work in this thesis studies two principal themes in this transformation: uncertainty and decentralization.</p>
<p>Uncertainty is a key challenge in the modern grid resulting from the weather dependence of variable renewables and volatile loads like electric vehicles distributed throughout the grid. Electricity markets, whose function is to regulate the precise balance of supply and demand across the system, face a pressing need for dispatch mechanisms that account for uncertainty while providing participation incentives for generators and loads. We introduce a framework for multi-stage market dispatch and pricing under a general description of forecast uncertainty that enables system operators to explicitly incorporate uncertainty into market-clearing prices. In related work, we study mechanisms that guarantee feasibility of multi-interval dispatch under robust uncertainty and provide participation incentives for shiftable demand response in forward multi-interval markets.</p>
<p>The trend towards a more decentralized energy system stems from the inherent modularity of distributed energy resources (DERs), such as solar and storage, as well as the persistent growth in end-use loads. This evolution presents significant challenges to system operators who typically lack the tools and processes for managing a complex, distributed power system. To fill this gap, we introduce and implement a Microgrid Operating System (OS), a software platform for monitoring, modeling, and optimizing microgrids and distribution systems. The Microgrid OS is a central layer that links DER hardware, such as batteries, solar, and flexible loads, to energy applications like cost minimization, emissions reduction, and wholesale market participation. The core functions it provides are data acquisition and processing, system modeling and learning, and optimization and control. We present key modules of the Microgrid OS in the context of several implementation projects in microgrids, commercial buildings, and distribution networks.</p>https://thesis.library.caltech.edu/id/eprint/16114Distributed Control Theory for Biological and Cyberphysical Systems
https://resolver.caltech.edu/CaltechTHESIS:07062023-214417026
Authors: {'items': [{'email': 'js.lisa.li@gmail.com', 'id': 'Li-Jing-Shuang-Lisa', 'name': {'family': 'Li', 'given': 'Jing Shuang (Lisa)'}, 'orcid': '0000-0003-4931-8709', 'show_email': 'YES'}]}
Year: 2024
DOI: 10.7907/p3k0-rv78
In engineering, control theory plays a crucial role in the design and analysis of robust and efficient systems --- including robots, spacecraft, and power grids. In biology, control theory underlies sensorimotor and locomotion models of organisms. Distributed control is particularly useful for large-scale cyber-physical systems and also in biological systems, where communication is more limited than in engineered counterparts. In this thesis, I provide a number of theoretical advances in distributed control theory on the relationship between communication within controllers vs. closed-loop behavior in both the online and offline settings, on the application of distributed methods to robust control, and on necessarily information flow within controllers subject to communication constraints. I then discuss the applications of these theoretical advances to the primate cortex, as well as to sensorimotor models of drosophila locomotion. Overall, the contributions outlined in this thesis facilitate modeling techniques and insights that were previously unavailable.https://thesis.library.caltech.edu/id/eprint/16137