Optimal control theory concerns the study of dynamical systems where one operates a control parameter with the goal of optimizing a given payoff function. This textbook provides an accessible, examples-led approach to the subject. The text focuses on systems modeled by differential equations, with applications drawn from a wide range of topics, including engineering, economics, finance, and game theory. Each topic is complemented by carefully prepared exercises to enhance understanding. The book begins with introductory chapters giving an overview of the subject and covering the necessary optimization techniques from calculus. After this, Pontryagin's method is developed for control problems on one-dimensional state spaces, culminating in the study of linear-quadratic systems. The core material is rounded out by the consideration of higher-dimensional systems. The text concludes with more advanced topics such as bang-bang controls and differential game theory. A final chapter examines the calculus of variations, giving a brief overview of the Euler-Lagrange theory and general isoperimetric problems. Designed for undergraduates in mathematics, physics, or economics, Optimal Control Theory can be used in a structured course or for self-study. The treatment is highly accessible and only requires a familiarity with multivariable calculus, differential equations, and basic matrix algebra.
- 242 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
About this book
Information
Subtopic
Mathematics GeneralIndex
MathematicsTable of contents
- Cover
- Title page
- Copyright
- Contents
- Introduction
- Chapter 1. Getting Started
- Chapter 2. Static Optimization
- Chapter 3. Control: A Discrete Start
- Chapter 4. First Principle
- Chapter 5. Unpacking Pontryagin
- Chapter 6. Easing the Restrictions
- Chapter 7. Linear-Quadratic Systems
- Chapter 8. Two Dimensions
- Chapter 9. Targets
- Chapter 10. Switching Controlsand Stationarity
- Chapter 11. Time, Value, and Hamilton-Jacobi-Bellman Equation
- Chapter 12. Differential Games
- Chapter 13. Calculus of Variations
- Appendix A. Table of Principles
- Appendix B. Two-DimensionalLinear Systems
- Appendix C. Hints
- Appendix D. Solutions
- Bibliography
- Index
- Back Cover
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Yes, you can access Optimal Control by Stewart Johnson in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.