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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 01:46:46 +0000Constrained Finite Receding Horizon Linear Quadratic Control
https://resolver.caltech.edu/CaltechCDSTR:1997.002
Authors: {'items': [{'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}, {'id': 'Nevistić-V', 'name': {'family': 'Nevistić', 'given': 'Vesna'}}]}
Year: 1993
Issues of feasibility, stability and performance are considered for a finite horizon formulation of receding horizon control (RHC) for linear systems under mixed linear state and control constraints. It is shown that for a sufficiently long horizon, a receding horizon policy will remain feasible and result in stability, even when no end constraint is imposed. In addition, offline finite horizon calculations can be used to determine not only a stabilizing horizon length, but guaranteed performance bounds for the receding horizon policy. These calculations are demonstrated on two examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/swp5b-88q49Nonlinear Games: examples and counterexamples
https://resolver.caltech.edu/CaltechAUTHORS:20140527-071022483
Authors: {'items': [{'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John'}, 'orcid': '0000-0002-1828-2486'}, {'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}, {'id': 'Shapiro-B', 'name': {'family': 'Shapiro', 'given': 'Benjamin'}}, {'id': 'Nevistić-V', 'name': {'family': 'Nevistić', 'given': 'Vesna'}}]}
Year: 1996
DOI: 10.1109/CDC.1996.577292
Popular nonlinear control methodologies are compared using benchmark examples generated with a "converse Hamilton-Jacobi-Bellman" method (CoHJB). Starting with the cost and optimal value function V, CoHJB solves HJB PDEs "backwards" algebraically to produce nonlinear dynamics and optimal controllers and disturbances. Although useless for design, it is great for generating benchmark examples. It is easy to use, computationally tractable, and can generate essentially all possible nonlinear optimal control problems. The optimal control and disturbance are then known and can be used to study actual design methods, which must start with the cost and dynamics without knowledge of V. This paper gives a brief introduction to the CoHJB method and some of the ground rules for comparing various methods. Some very simple examples are given to illustrate the main ideas. Both Jacobian linearization and feedback linearization combined with linear optimal control are used as "strawmen" design methods.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xg6y0-9gr72Optimality of nonlinear design techniques: A converse HJB approach
https://resolver.caltech.edu/CaltechCDSTR:1996.022
Authors: {'items': [{'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}, {'id': 'Nevistić-V', 'name': {'family': 'Nevistić', 'given': 'Vesna'}}]}
Year: 1996
The issue of optimality in nonlinear controller design is confronted by using the converse HJB approach to classify dynamics under which certain design schemes are optimal. In particular, the techniques of Jacobian linearization, pseudo-Jacobian linearization, and feedback linearization are analyzed. Finally, the conditions for optimality are applied to the 2-D nonlinear oscillator, where simple, nontrivial examples are produced in which the various design techniques are optimal.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/atw6s-v6d95Constrained nonlinear optimal control: a converse HJB approach
https://resolver.caltech.edu/CaltechCDSTR:1996.021
Authors: {'items': [{'id': 'Nevistić-V', 'name': {'family': 'Nevistić', 'given': 'Vesna'}}, {'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}]}
Year: 1996
Extending the concept of solving the Hamilton-Jacobi-Bellman (HJB) optimization equation backwards [2], the so called converse constrained optimal control problem is introduced, and used to create various classes of nonlinear systems for which the optimal controller subject to constraints is known. In this way a systematic method for the testing, validation and comparison of different control techniques
with the optimal is established. Because it naturally and explicitly handles constraints, particularly control input saturation, model predictive control (MPC) is a potentially powerful approach for nonlinear control design. However, nonconvexity of the nonlinear programs (NLP) involved in the MPC optimization makes the solution problematic. In order to explore properties of MPC-based constrained control schemes, and to point out the potential issues in implementing MPC, challenging benchmark examples are generated and analyzed. Properties of MPC-based constrained techniques are then evaluated and implementation issues are explored by applying both nonlinear MPC and MPC with feedback linearization.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/r1ntm-2p548Finite Receding Horizon Linear Quadratic Control: A Unifying Theory for Stability and Performance Analysis
https://resolver.caltech.edu/CaltechCDSTR:1997.001
Authors: {'items': [{'id': 'Nevistić-V', 'name': {'family': 'Nevistić', 'given': 'Vesna'}}, {'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}]}
Year: 1997
We consider a finite horizon based formulation of receding horizon control for linear discrete-time plants with quadratic costs. A framework is developed for analyzing stability and performance of finite receding horizon control for arbitrary terminal weights. Previous stability and performance results, including end constraints, infinite horizon formulations, and the fake algebraic Riccati equation, arc all shown to be special cases of the derived results. The unconstrained case is presented, where conditions for finite receding horizon control to be stabilizing and within specified bounds of the optimal infinite horizon performance can be computed from the solution to the Riccati difference equations. Nevertheless, the framework presented is general in that it lays the groundwork for extension to constrained systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v7xhd-6bp33On receding horizon extensions and control Lyapunov functions
https://resolver.caltech.edu/CaltechAUTHORS:20190315-104922109
Authors: {'items': [{'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}, {'id': 'Nevistić-V', 'name': {'family': 'Nevistić', 'given': 'Vesna'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John C.'}, 'orcid': '0000-0002-1828-2486'}]}
Year: 1998
DOI: 10.1109/ACC.1998.703180
Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control (RHC) to develop a new class of control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a control Lyapunov function based receding horizon scheme, of which a special case provides an appropriate extension of a variation on Sontag's formula. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mcwtt-mmb40A receding horizon generalization of pointwise min-norm controllers
https://resolver.caltech.edu/CaltechAUTHORS:PRIieeetac00
Authors: {'items': [{'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}, {'id': 'Nevistić-V', 'name': {'family': 'Nevistić', 'given': 'Vesna'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John C.'}, 'orcid': '0000-0002-1828-2486'}]}
Year: 2000
DOI: 10.1109/9.855550
Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a CLF based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuous-time receding horizon control law. The issue of implementation under discrete-time sampling is then discussed as a modification. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem. Finally, stronger connections to both optimal and pointwise min-norm control are proved.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kgmzr-kdj81Kuhn-Tucker-based stability conditions for systems with saturation
https://resolver.caltech.edu/CaltechAUTHORS:PRIieeetac01
Authors: {'items': [{'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}, {'id': 'Gianelli-M', 'name': {'family': 'Gianelli', 'given': 'Monica'}}]}
Year: 2001
DOI: 10.1109/9.956065
This paper presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented can be extended to handle a dead-zone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn-Tucker) conditions for optimality are used to derive linear and quadratic constraints which characterize the saturation. After selecting a candidate Lyapunov function, we pose the question of whether the Lyapunov function is decreasing along trajectories of the system as an implication between the necessary conditions derived from the saturation optimization, and the time derivative of the Lyapunov function. This leads to stability conditions in terms of linear matrix inequalities, which are obtained by an application of the S-procedure to the implication. An example is provided where the proposed technique is compared and contrasted with previous analysis methods.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nwbry-a2s05