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Problems and Methods of Optimal Control

  • Book
  • © 1994

Overview

Authors:
  1. Leonid D. Akulenko

    1. Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 286)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
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  2. Averaging Method in Optimal Control Problems for Quasilinear Oscillatory Systems

    • Leonid D. Akulenko
    Pages 1-45

  3. The Foundation of Asymptotic Methods for Controlled Quasilinear Systems and Some Generalizations

    • Leonid D. Akulenko
    Pages 46-96

  4. Averaging Method in Optimal Control Problems for Single-Frequency Essentially Nonlinear Systems

    • Leonid D. Akulenko
    Pages 97-134

  5. The Foundation of Asymptotic Methods of the Separation of Motions in Essentially Nonlinear Controlled Systems

    • Leonid D. Akulenko
    Pages 135-158

  6. Control of Motions of “Pendulum-Type” Systems

    • Leonid D. Akulenko
    Pages 159-198

  7. Optimal Control of Orbital Motions and Rotations of Spacecrafts Using “Low Thrust”

    • Leonid D. Akulenko
    Pages 199-222

  8. Approximate Synthesis of Optimal Control for Perturbed Systems with Invariant Norm

    • Leonid D. Akulenko
    Pages 223-280

  9. Other Prospects for Developing Methods of Optimal Control Synthesis

    • Leonid D. Akulenko
    Pages 281-332

  10. Back Matter

    Pages 333-344
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Keywords

About this book

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).

Authors and Affiliations

  • Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    Leonid D. Akulenko

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