Problems and Methods of Optimal Control

By: L.D. Akulenko

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Hardcover | 1 May 1994

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364 Pages

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The numerous applications of optimal control theory have given an incentive to the development of approximate techniques aimed at the construction of control laws and the optimization of dynamical systems. These constructive approaches rely on small parameter methods (averaging, regular and singular perturbations), which are well-known and have been proven to be efficient in nonlinear mechanics and optimal control theory (maximum principle, variational calculus and dynamic programming). An essential feature of the procedures for solving optimal control problems consists in the necessity for dealing with two-point boundary-value problems for nonlinear and, as a rule, nonsmooth multi-dimensional sets of differential equations. This circumstance complicates direct applications of the above-mentioned perturbation methods which have been developed mostly for investigating initial-value (Cauchy) problems. There is now a need for a systematic presentation of constructive analytical per turbation methods relevant to optimal control problems for nonlinear systems. The purpose of this book is to meet this need in the English language scientific literature and to present consistently small parameter techniques relating to the constructive investigation of some classes of optimal control problems which often arise in prac tice. This book is based on a revised and modified version of the monograph: L. D. Akulenko "Asymptotic methods in optimal control". Moscow: Nauka, 366 p. (in Russian).

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Preface
Averaging Method in Optimal Control Problems for Quasilinear Oscillatory Systems	p. 1
The Foundation of Asymptotic Methods for Controlled Quasilinear Systems and Some Generalizations	p. 46
Averaging Method in Optimal Control Problems for Single-Frequency Essentially Nonlinear Systems	p. 97
The Foundation of Asymptotic Methods of the Separation of Motions in Essentially Nonlinear Controlled Systems	p. 135
Control of Motions of "Pendulum-Type" Systems	p. 159
Optimal Control of Orbital Motions and Rotations of Spacecrafts Using "Low Thrust"	p. 199
Approximate Synthesis of Optimal Control for Perturbed Systems with Invariant Norm	p. 223
Other Prospects for Developing Methods of Optimal Control Synthesis	p. 281
References	p. 333
Key Index	p. 339
Table of Contents provided by Blackwell. All Rights Reserved.

Problems and Methods of Optimal Control

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