Essays on Pareto Optimality in Cooperative Games

The book focuses on Pareto optimality in cooperative games. Most of the existing works focus on the Pareto optimality of deterministic continuous-time systems or for the regular convex LQ case. To expand on the available literature, we explore the existence conditions of Pareto solutions in stochastic differential game for more general cases. In addition, the LQ Pareto game for stochastic singular systems, Pareto-based guaranteed cost control for uncertain mean-field stochastic systems, and the existence conditions of Pareto solutions in cooperative difference game are also studied in detail.

Addressing Pareto optimality for more general cases and wider systems is one of the major features of the book, making it particularly suitable for readers who are interested in multi-objective optimal control. Accordingly, it offers a valuable asset for researchers, engineers, and graduate students in the fields of control theory and control engineering, economics, management science,mathematics, etc.

Studies Pareto optimality in stochastic differential game and difference game Presents the LQ Pareto game for stochastic singular systems Focuses on the Pareto-based guaranteed cost control problem for uncertain mean-field stochastic systems

Auteur

Yaning Lin received the M.S. degree in operations research and cybernetics from Shandong University, Jinan, China, and the Ph.D. degree in control theory and control engineering from Shandong University of Science and Technology, Qingdao, China, in 2008 and 2018, respectively. She is currently an associate professor with the Shandong University of Technology, Zibo, China. Her main research interests include game theory, stochastic systems, descriptor systems and optimal control. Weihai Zhang received the M.S. degree in probability theory and mathematical statistics from Hangzhou University (now Zhejiang University), Hangzhou, China, and the Ph.D. degree in operations research and cybernetics from Zhejiang University, Hangzhou, China, in 1994 and 1998, respectively. He is currently a Professor with the Shandong University of Science and Technology, Qingdao, China. He has authored and co-authored more than 110 peer-reviewed journal papers and one monograph Stochastic H2/H8 Control: A Nash Game Approach (Boca Raton, FL, USA: CRC Press, 2017). His research interests include linear and nonlinear stochastic optimal control, mean-field systems, robust H8 control, stochastic stability and stabilization, multi-objective optimization, and fuzzy adaptive control. Dr. Zhang is a Member of Technical Committee on Control Theory of the Chinese Association of Automation. He received the second prize of the Ministry of Education of the People's Republic of China twice. He is a Taishan Scholar of Shandong Province of China, and serves as an Associate Editor for the Asian Journal of Control and Journal of the Franklin Institute.

Résumé
"The book provides a concise, clear summary of its subject matter. It will be a valuable reference for researchers looking to apply models of cooperative dynamic games in their work." (Thomas Wiseman, zbMATH 1519.91003, 2023)

Contenu
Introduction.- Existence conditions of Pareto solutions in the finite horizon stochastic differential game.- Existence conditions of Pareto solutions in the infinite horizon stochastic differential game.- LQ Pareto game of the stochastic singular systems in finite horizon.- LQ Pareto game of the stochastic singular systems in infinite horizon.- Pareto-based guaranteed cost control of the uncertain mean-field stochastic systems.- Existence conditions of Pareto solutions in the finite horizon cooperative difference game.- Existence conditions of Pareto solutions in the infinite horizon cooperative difference game.- References.