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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 contentto 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
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 contentto 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
"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)
"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)