(PHD, 1970)

Abstract:

H. J. Kushner has obtained the differential equation satisfied by the optimal feedback control law for a stochastic control system in which the plant dynamics and observations are perturbed by independent additive Gaussian white noise processes. However, the differentiation includes the first and second functional derivatives and, except for a restricted set of systems, is too complex to solve with present techniques.

This investigation studies the optimal control law for the open loop system and incorporates it in a sub-optimal feedback control law. This suboptimal control law’s performance is at least as good as that of the optimal control function and satisfies a differential equation involving only the first functional derivative. The solution of this equation is equivalent to solving two two-point boundary valued integro-partial differential equations. An approximate solution has advantages over the conventional approximate solution of Kushner’s equation.

As a result of this study, well known results of deterministic optimal control are deduced from the analysis of optimal open loop control.

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(PHD, 1969)

Abstract:

A mathematical model is proposed in this thesis for the control mechanism of free fatty acid-glucose metabolism in healthy individuals under resting conditions. The objective is to explain in a consistent manner some clinical laboratory observations such as glucose, insulin and free fatty acid responses to intravenous injection of glucose, insulin, etc. Responses up to only about two hours from the beginning of infusion are considered. The model is an extension of the one for glucose homeostasis proposed by Charette, Kadish and Sridhar (Modeling and Control Aspects of Glucose Homeostasis. Mathematical Biosciences, 1969). It is based upon a systems approach and agrees with the current theories of glucose and free fatty acid metabolism. The description is in terms of ordinary differential equations. Validation of the model is based on clinical laboratory data available at the present time. Finally procedures are suggested for systematically identifying the parameters associated with the free fatty acid portion of the model.

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(PHD, 1969)

Abstract: The relations among organs and processes resulting in the hormonal control of human metabolism are interpreted mathematically for the derivation and analysis of models using control systems theory and systems engineering techniques. A dynamic nonlinear model for glucose homeostasis including four controlling hormones is derived from the current biological knowledge of the normal system and simulated for comparison with experimental data. Mathematical algorithms are developed and demonstrated for the identification of the parameters of the proposed model and a series of experiments is proposed to yield the minimal requisite data for the application of the method. Control systems analyses are undertaken on the proposed model to demonstrate a consistent methodology for investigations of complex metabolic control systems in the intact animal

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(PHD, 1969)

Abstract:

Minimum-energy control problems for various electric propulsion vehicles are formulated and solved using modern control theory and systems engineering techniques. Analytical results are obtained by making several simplifications and approximations in the dynamical equations of each system whose performance index is related to the minimization of the system energy consumption for a required control action. An attempt is made to implement the resulting control laws using the current engineering practice.

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(PHD, 1969)

Abstract: The low-thrust guidance problem is defined as the minimum terminal variance (MTV) control of a space vehicle subjected to random perturbations of its trajectory. To accomplish this control task, only bounded thrust level and thrust angle deviations are allowed, and these must be calculated based solely on the information gained from noisy, partial observations of the state. In order to establish the validity of various approximations, the problem is first investigated under the idealized conditions of perfect state information and negligible dynamic errors. To check each approximate model, an algorithm is developed to facilitate the computation of the open loop trajectories for the nonlinear bang-bang system. Using the results of this phase in conjunction with the Ornstein-Uhlenbeck process as a model for the random inputs to the system, the MTV guidance problem is reformulated as a stochastic, bang-bang, optimal control problem. Since a complete analytic solution seems to be unattainable, asymptotic solutions are developed by numerical methods. However, it is shown analytically that a Kalman filter in cascade with an appropriate nonlinear MTV controller is an optimal configuration. The resulting system is simulated using the Monte Carlo technique and is compared to other guidance schemes of current interest.

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(PHD, 1969)

Abstract: Re-entry trajectory design problem of a space capsule into the Martian atmosphere is investigated within the context of modern control theory. The optimal control law which minimizes the heat generated on the surface of the capsule is obtained analytically. This in turn allows the capsule to make a successful softlanding on Mars through the partially known atmosphere of the planet. The investigation is also extended to the guidance of the capsule in a stochastic disturbance environment. An attempt is made to simplify the stochastic control law so that the mechanization of the resulting control law is within the grasp of current engineering technology.

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