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.
Author(s): Yaning Lin, Weihai Zhang
Publisher: Springer
Year: 2022
Language: English
Pages: 168
City: Singapore
Preface
Acknowledgements
Contents
Acronyms
1 Introduction
1.1 Background
1.2 Pareto Optimality
1.3 Research Status
1.3.1 Research Status of Pareto Optimality in Cooperative Differential Games
1.3.2 Research Status of Difference Games
References
2 Existence Conditions of Pareto Solutions in Finite Horizon Stochastic Differential Games
2.1 Introduction
2.2 Nonlinear Case
2.2.1 Necessary Conditions
2.2.2 Sufficient Conditions
2.3 LQ Case
2.3.1 Open-Loop Solution
2.3.2 Closed-Loop Solution
2.4 Examples
2.5 Conclusions
References
3 Existence Conditions of Pareto Solutions in Infinite Horizon Stochastic Differential Games
3.1 Introduction
3.2 Nonlinear Case
3.2.1 Necessary Conditions
3.2.2 Sufficient Conditions
3.3 LQ Case
3.3.1 Open-Loop Solution
3.3.2 Closed-Loop Solution
3.4 Examples
3.5 Conclusions
References
4 LQ Pareto Game of the Stochastic Singular Systems in Finite Horizon
4.1 Introduction
4.2 Finite Horizon LQ Optimal Control of the Stochastic Singular Systems
4.3 Finite Horizon Stochastic Singular LQ Pareto Game
4.4 Examples
4.5 Conclusions
References
5 LQ Pareto Game of the Stochastic Singular Systems in Infinite Horizon
5.1 Introduction
5.2 Indefinite Infinite Horizon LQ Optimal Control …
5.3 Infinite Horizon Stochastic Singular LQ Pareto Game
5.4 Examples
5.5 Conclusions
References
6 Pareto-Based Guaranteed Cost Control of the Uncertain Mean-Field Stochastic Systems
6.1 Introduction
6.2 Preliminaries
6.3 Pareto Game of the Nominal Mean-Field Stochastic Systems
6.4 Pareto-Based Guaranteed Cost Control of the Uncertain …
6.5 LMI Approach
6.6 Examples
6.7 Conclusions
References
7 Pareto Optimality in Finite Horizon Cooperative Difference Games
7.1 Introduction
7.2 Nonlinear Case
7.2.1 Necessary Conditions
7.2.2 Sufficient Conditions
7.3 LQ Case
7.3.1 Open-Loop Solution
7.3.2 Closed-Loop Solution
7.4 Examples
7.5 Conclusions
References
8 Pareto Optimality in Infinite Horizon Cooperative Difference Games
8.1 Introduction
8.2 Nonlinear Case
8.2.1 Necessary Conditions
8.2.2 Sufficient Conditions
8.3 LQ Case
8.3.1 Open-Loop Solution
8.3.2 Closed-Loop Solution
8.4 Examples
8.5 Conclusions
References
Index
