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
