Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems: Regularization Approach (Static & Dynamic Game Theory: Foundations & Applications) - Softcover

Über die Autorin bzw. den Autor

Valery Y. Glizer received his Ph.D. in mathematics and physics in 1980. From 2007-2020, he served as an Associate/Full Professor at the Department of Mathematics in the ORT Braude College of Engineering, Karmiel, Israel. Currently, Prof. Glizer serves as a researcher at The Galilee Research Center for Applied Mathematics, ORT Braude College of Engineering, Karmiel, Israel. His main areas of research are dynamic games, optimal control, robust control, singular perturbations, systems theory and time delay systems.
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.

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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.