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Introduction to Optimal Control Theory : Undergraduate Texts in Mathematics - Jack Macki

Introduction to Optimal Control Theory

Undergraduate Texts in Mathematics


Published: 9th May 1995
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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.

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.

ISBN: 9780387906249
ISBN-10: 038790624X
Series: Undergraduate Texts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 168
Published: 9th May 1995
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 1.27
Weight (kg): 0.44
Edition Number: 2