Author | Macki, Jack. author |
---|---|
Title | Introduction to Optimal Control Theory [electronic resource] / by Jack Macki, Aaron Strauss |
Imprint | New York, NY : Springer New York, 1982 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5671-7 |
Descript | XIV, 168 p. online resource |
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 ControlsโThe 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 VโA Proof of the Pontryagin Maximum Principle -- Mathematical Appendix