Optimal Control

This textbook provides a comprehensive introduction to optimal control theory, covering linear and nonlinear systems. It includes two new chapters and several improvements, with problem sets and additional tasks for students to master the subject.

Format: Hardback
Length: 251 pages
Publication date: 13 January 2022
Publisher: Springer Nature Switzerland AG

This textbook, now in its second edition, is the result of lectures, practical problems, and workshops on optimal control delivered by the authors at Irkutsk State University, Far Eastern Federal University (both in Vladivostok, Russia), and Kwangwoon University (Seoul, South Korea). In this comprehensive work, the authors delve into the theory of linear and nonlinear systems, exploring the fundamental challenge of establishing the necessary and sufficient conditions for optimal processes. Readers will find two new chapters, offering results of potential interest to researchers specializing in optimal control theory and those with an interest in applications in engineering and related sciences. Furthermore, numerous improvements have been made throughout the text to enhance its readability and usefulness.

The book is organized into three parts. Part I provides a gentle introduction to the basic concepts in optimal control, laying the foundation for the subsequent chapters. Part II builds upon the separation theorem and the concept of a reachability set, constructing the theory of linear control systems. The authors demonstrate the closure of the reachability set in the class of piecewise continuous controls and address issues such as controllability, observability, identification, performance, and terminal control. Part III, in turn, focuses on nonlinear control systems. Employing the method of variations and the Lagrange multipliers of nonlinear problems, the authors prove the Pontryagin maximum principle for problems involving mobile ends of trajectories.

Problem sets at the end of each chapter and a list of additional tasks, provided in the appendix, are offered to students seeking to master the subject. These exercises have been carefully chosen not only to reinforce the theoretical understanding but also to encourage the application of such knowledge in more advanced problems.

By presenting a comprehensive and up-to-date treatment of optimal control, this textbook serves as a valuable resource for students, researchers, and practitioners in the field. Its extensive coverage, coupled with practical examples and exercises, makes it an essential tool for anyone seeking to deepen their knowledge and expertise in this dynamic and interdisciplinary area.

Weight: 576g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030910280
Edition number: 2nd ed. 2021