An Introduction to Optimal Control Theory: The Dynamic Programming Approach

This book provides a concise and systematic presentation of optimal control theory for large families of deterministic and stochastic systems with discrete or continuous time parameters. It focuses on the dynamic programming technique and is suitable for undergraduate students with basic calculus and linear algebra knowledge, as well as advanced undergraduates and graduate students with mathematical analysis and stochastic processes expertise.

Format: Paperback / softback
Length: 273 pages
Publication date: 08 March 2024
Publisher: Springer International Publishing AG

This comprehensive book delves into the realm of optimal control problems, catering to a wide array of deterministic and stochastic systems with discrete or continuous time parameters. Spanning various disciplines such as Economics, Engineering, Operations Research, and Management Science, among others, it aims to provide a concise, systematic, and self-contained presentation of key topics in optimal control theory. The foundation of the analyses is rooted in the dynamic programming (DP) technique, a versatile tool applicable to almost all control problems encountered in theory and applications.

The book begins with a general introduction to control problems, dividing the topic into four distinct parts: control of discrete-time deterministic systems, discrete-time stochastic systems, ordinary differential equations, and a comprehensive continuous-time MCP with applications for stochastic differential equations. The first and second parts are designed to be accessible to undergraduate students with a solid foundation in elementary calculus, linear algebra, and some concepts from probability theory. These sections lay the groundwork for understanding the fundamentals of control theory and its applications.

On the other hand, the third and fourth parts cater to advanced undergraduates and graduate students who possess a working knowledge of mathematical analysis, including derivatives, integrals, and stochastic processes. These parts delve deeper into the complexities of optimal control theory and offer insights into advanced topics such as dynamic programming, optimal control algorithms, and their applications in various fields.

Throughout the book, numerous examples and exercises are provided to reinforce the theoretical concepts and aid in understanding the practical applications of optimal control theory. Each chapter concludes with a summary, review questions, and suggested readings, allowing students to further explore the topics and deepen their knowledge.

In summary, this book serves as an invaluable resource for students, researchers, and practitioners interested in optimal control theory. It provides a comprehensive coverage of key topics, employs a practical approach, and is accompanied by ample examples and exercises to facilitate a thorough understanding of the subject matter. Whether you are a beginner seeking to foray into the world of control theory or an advanced student seeking to expand your expertise, this book will undoubtedly be a valuable asset in your academic journey.

Dimension: 235 x 155 (mm)
ISBN-13: 9783031211416
Edition number: 1st ed. 2023