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

This book presents a comprehensive analysis of singular differential games and H∞ control problems, utilizing a regularization approach for innovative solutions.

This monograph focuses on the analysis and resolution of singular differential games and singular H∞ control problems, applicable in both finite- and infinite-horizon contexts. Building upon the authors' previous research, Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems is groundbreaking in its approach, being the first to tackle these singular issues through regularization techniques. The text is structured to facilitate understanding, offering a comprehensive exploration of the subject matter.

Commencing with a brief introduction, the authors outline solvability conditions for regular differential games and H∞ control problems. The subsequent chapter delves into the singular finite-horizon linear-quadratic differential game, employing the regularization method to derive solutions. This method is further extended to address infinite-horizon scenarios, showcasing its versatility. The final chapters are dedicated to singular finite-horizon and infinite-horizon linear-quadratic H∞ control problems, providing both theoretical insights and practical examples to demonstrate the applicability of the results.

Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems is meticulously organized, allowing readers to engage with each chapter independently or as a cohesive whole. Each section features its own introduction, notation list, literature review, and bibliography, enhancing the text's self-contained nature. Detailed proofs are thoughtfully included in separate subsections for improved clarity. This work is essential for researchers and engineers in applied mathematics, dynamic games, control engineering, and related fields, and serves as a valuable reference for graduate students.