Machine generated contents note: 1. Introduction -- 1.1. Outline -- 1.2. Prerequisites -- 1.3. Brief History of Optimal Control -- 1.4. Notes -- 2. Ordinary Differential Equations -- 2.1. Overview -- 2.2. First-Order ODEs -- 2.3. Higher-Order ODEs and Solution Techniques -- 2.4. Notes -- 2.5. Exercises -- 3. Optimal Control Theory -- 3.1. Overview -- 3.2. Control Systems -- 3.3. Optimal Control -- A Motivating Example -- 3.4. Finite-Horizon Optimal Control -- 3.5. Infinite-Horizon Optimal Control -- 3.6. Supplement 1: A Proof of the Pontryagin Maximum Principle -- 3.7. Supplement 2: The Filippov Existence Theorem -- 3.8. Notes -- 3.9. Exercises -- 4. Game Theory -- 4.1. Overview -- 4.2. Fundamental Concepts -- 4.3. Differential Games -- 4.4. Notes -- 4.5. Exercises -- 5. Mechanism Design -- 5.1. Motivation -- 5.2. Model with Two Types -- 5.3. Screening Problem -- 5.4. Nonlinear Pricing -- 5.5. Notes -- 5.6. Exercises -- Appendix A Mathematical Review -- A.1. Algebra -- A.2. Normed Vector Spaces -- A.3. Analysis -- A.4. Optimization -- A.5. Notes -- Appendix B Solutions to Exercises -- B.1. Numerical Methods -- B.2. Ordinary Differential Equations -- B.3. Optimal Control Theory -- B.4. Game Theory -- B.5. Mechanism Design -- Appendix C Intellectual Heritage
Summary
A rigorous introduction to optimal control theory, with an emphasis on applications in economics. Appendices provide a mathematical review and full solutions to all end-of-chapter problems
