Overview
- First text to study singular differential games and $H_{\inf}$ control problems using the regularization approach
- Presents material in self-contained chapters, allowing them to be studied independently or in order
- Illustrates results using theoretical and real-world examples
Part of the book series: Static & Dynamic Game Theory: Foundations & Applications (SDGTFA)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
After a brief introduction, solvability conditions are presented for the regular differential games and $H_{\inf}$ control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic $H_{\inf}$ control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text,and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections.
Singular Linear-Quadratic Zero-Sum Differential Games and $H_{\inf}$ Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these area
Reviews
“The present book formulates the theoretical analysis of the singular games and provides academic and real life examples which illustrate the theoretical results and their applicability. This book is of great interest and importance for researchers working in applied mathematics, control theory, mechanical engineering and biology.” (Savin Treanta, zbMATH 1504.49001, 2023)
Authors and Affiliations
About the authors
Oleg Kelis received his M.Sc. in mathematics (with highest honors) in 2008 and his Ph.D. in 2019. Currently Dr. Kelis serves as an adjunct lecturer at the Department of Mathematics, Ort Braude College of Engineering, Karmiel, Israel, and at the Faculty of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel. His fields of research are differential games, optimal control, singularly perturbed problems.
Bibliographic Information
Book Title: Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems
Book Subtitle: Regularization Approach
Authors: Valery Y. Glizer, Oleg Kelis
Series Title: Static & Dynamic Game Theory: Foundations & Applications
DOI: https://doi.org/10.1007/978-3-031-07051-8
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-07050-1Published: 30 August 2022
Softcover ISBN: 978-3-031-07053-2Published: 31 August 2023
eBook ISBN: 978-3-031-07051-8Published: 29 August 2022
Series ISSN: 2363-8516
Series E-ISSN: 2363-8524
Edition Number: 1
Number of Pages: X, 206
Number of Illustrations: 2 b/w illustrations, 1 illustrations in colour
Topics: Game Theory, Economics, Social and Behav. Sciences, Systems Theory, Control