Optimal Control: A Differential Equations Approach (AMS/MAA Textbooks) - Softcover

Stewart Johnson

Softcover

ISBN 10: 1470477831 ISBN 13: 9781470477837

Publisher: American Mathematical Society, 2025

Synopsis

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.

About this title

About the Author

Stewart Johnson, Williams College, Williamstown, Massachusetts.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2025
• Language: English
• ISBN 10: 1470477831
• ISBN 13: 9781470477837
• Binding: Paperback
• Number of pages: 225