Singular Linear-Quadratic Zero-Sum Differential Games and H Control Problems

This monograph is devoted to the analysis and solution of singular differential games and singular $H_{\inf}$ control problems in both finite- and infinite-horizon settings. Expanding on the authors' previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach.
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

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

Auteur

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.

Résumé
"The book seems to be well structured and comprehensible, in that each chapter contains the same approach to the analysis ... type of games, so that readability is guaranteed ... . each chapter contains a section including some concluding remarks and a related literature review. The introduction of the book is quite short and basically presents the history of the class of games to be treated, together with a rich overview of the recent contributions in the applied mathematics literature." (Arsen Palestini, Mathematical Reviews, May, 2023)
"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)

Contenu
Introduction.- Examples of Singular Extremal Problems and Some Basic Notions.- Preliminaries.- Singular Finite-Horizon Zero-Sum Dierential Game.- Singular Innite-Horizon Zero-Sum Dierential Game.- Singular Finite-Horizon $H{\inf}$ Problem.- Singular Innite-Horizon $H{\inf}$ Problem.