Optimal Control
A Differential Equations Approach
Seiten
2025
American Mathematical Society (Verlag)
978-1-4704-7783-7 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-7783-7 (ISBN)
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Explores the dynamics of controlled systems to optimize outcomes using differential equations. The text presents core techniques, Pontryagin’s method, linear-quadratic models, and higher-dimensional challenges, while also addressing bang-bang controls, differential games, and Euler-Lagrange theory alongside practical exercises.
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.
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.
Stewart Johnson, Williams College, Williamstown, Massachusetts.
Getting started
Static optimization
Control: A discrete start
First principle
Unpacking Pontryagin
Easing the restrictions
Linear-quadratic systems
Two dimensions
Targets
Switching controls and stationarity
Time, value, and Hamilton-Jacobi-Bellman equation
Differential games
Calculus of variations
Table of principles
Two-dimensional linear systems
Hints
Solutions
Bibliography
Index
| Erscheint lt. Verlag | 18.12.2025 |
|---|---|
| Reihe/Serie | AMS/MAA Textbooks |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-4704-7783-1 / 1470477831 |
| ISBN-13 | 978-1-4704-7783-7 / 9781470477837 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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