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 ControlsThe 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 VA Proof of the Pontryagin Maximum Principle. - Mathematical Appendix. Language: English