Introduction to optimal control theory

Jack Macki, Aaron Strauss

This is an introduction to optimal control theory for systems governed by vector ordinary differential equations, up to and including a proof of the Pontryagin Maximum Principle. Though the subject is accessible to any student with a sound undergraduate mathematics background. Theory and applications are integrated with examples, particularly one special example (the rocket car) which relates all the abstract ideas to an understandable setting. The authors avoid excessive generalization, focusing rather on motivation and clear, fluid explanation.

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  • I Introduction and Motivation.- 1 Basic Concepts.- 2 Mathematical Formulation of the Control Problem.- 3 Controllability.- 4 Optimal Control.- 5 The Rocket Car.- Exercises.- Notes.- II Controllability.- 1 Introduction: Some Simple General Results.- 2 The Linear Case.- 3 Controllability for Nonlinear Autonomous Systems.- 4 Special Controls.- Exercises.- Appendix: Proof of the Bang-Bang Principle.- III Linear Autonomous Time-Optimal Control Problems.- 1 Introduction: Summary of Results.- 2 The Existence of a Time-Optimal Control
  • Extremal Controls
  • the Bang-Bang Principle.- 3 Normality and the Uniqueness of the Optimal Control.- 4 Applications.- 5 The Converse of the Maximum Principle.- 6 Extensions to More General Problems.- Exercises.- IV Existence Theorems for Optimal Control Problems.- 1 Introduction.- 2 Three Discouraging Examples. An Outline of the Basic Approach to Existence Proofs.- 3 Existence for Special Control Classes.- 4 Existence Theorems under Convexity Assumptions.- 5 Existence for Systems Linear in the State.- 6 Applications.- Exercises.- Notes.- V Necessary Conditions for Optimal Controls-The Pontryagin Maximum Principle.- 1 Introduction.- 2 The Pontryagin Maximum Principle for Autonomous Systems.- 3 Applying the Maximum Principle.- 4 A Dynamic Programming Approach to the Proof of the Maximum Principle.- 5 The PMP for More Complicated Problems.- Exercises.- Appendix to Chapter V-A Proof of the Pontryagin Maximum Principle.- Mathematical Appendix.

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書名 Introduction to optimal control theory
著作者等 Macki, Jack
Strauss, Aaron
シリーズ名 Undergraduate texts in mathematics
出版元 Springer-Verlag
刊行年月 c1982
版表示 1st ed. 1982. Corr. 2nd printing 1995
ページ数 xiii, 165 p.
大きさ 25 cm
ISBN 354090624X
NCID BA03509733
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言語 英語
出版国 アメリカ合衆国