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Table of Contents
Preface; Contents; Representation of Symbol; Content Introduction; 1 Introduction; 1.1 Research and Development Status of Generalized Markov Jump Linear System Theory; 1.1.1 Basic Model of Generalized Markov Jump Linear Systems; 1.1.2 Research Status of Generalized Markov Jump Systems; 1.2 Differential Games for the Generalized Markov Jump Linear Systems; 1.3 Contents of This Book; References; 2 Deterministic and Stochastic Differential Games; 2.1 Dynamic Optimization Techniques; 2.1.1 Dynamic Programming; 2.1.2 Optimal Control; 2.1.3 Stochastic Control.
2.2 Differential Games and Their Solution Concepts2.2.1 Open-Loop Nash Equilibria; 2.2.2 Closed-Loop Nash Equilibria; 2.2.3 Feedback Nash Equilibria; 2.3 Stochastic Differential Games and Their Solutions; 2.3.1 The Model of Stochastic Differential Game; 2.3.2 The Solutions of Stochastic Differential Game; 3 Stochastic Differential Games of Continuous-Time Markov Jump Linear Systems; 3.1 Stochastic LQ Problem-Differential Game with One Player; 3.1.1 Finite-Time Horizon Case; 3.1.1.1 Problem Formulation; 3.1.1.2 Main Results; 3.1.2 Infinite-Time Horizon Case; 3.1.2.1 Problem Formulation.
3.1.2.2 Main Results3.2 Stochastic Nash Differential Games with Two Player; 3.2.1 Finite-Time Horizon Case; 3.2.1.1 Problem Formulation; 3.2.1.2 Main Results; 3.2.2 Infinite-Time Horizon Case; 3.2.2.1 Problem Formulation; 3.2.2.2 Main Results; 3.2.3 Two Person Zero-Sum Stochastic Differential Game; 3.2.3.1 Finite-Time Horizon Case; 3.2.3.2 Infinite-Time Horizon Case; 3.2.4 Numerical Example; 3.3 Stochastic Stackelberg Differential Game with Two Person; 3.3.1 Problem Formulation; 3.3.2 Main Results; 3.4 Summary; References.
4 Stochastic Differential Game of Discrete-Time Markov Jump Linear Systems4.1 Stochastic LQ Problem-Differential Game with One Person; 4.1.1 Finite-Time Horizon; 4.1.1.1 Problem Formulation; 4.1.1.2 Main Results; 4.1.2 Infinite-Time Horizon; 4.2 Stochastic Nash Differential Games with Two Person; 4.2.1 Finite-Time Horizon; 4.2.1.1 Problem Formulation; 4.2.1.2 Main Result; 4.2.2 Infinite-Time Horizon; 4.2.2.1 Problem Formulation; 4.2.2.2 Main Result; 4.2.3 Two Person Zero-Sum Stochastic Differential Games; 4.2.3.1 Finite Time Horizon; 4.2.3.2 Infinite-Time Horizon.
4.3 Stackelberg Differential Games with Two Person4.3.1 Finite-Time Horizon; 4.3.1.1 Problem Formulation; 4.3.1.2 Main Result; 4.3.2 Infinite-Time Horizon; 4.4 Summary; References; 5 Stochastic Differential Game of Stochastic Markov Jump Singular Systems; 5.1 Stochastic LQ Problems-Differential Games of One Player; 5.1.1 Preliminaries; 5.1.1.1 Stability of the Stochastic Markov Jump Singular Systems; 5.1.2 LQ Problem of Stochastic Markov Jump Singular Systems; 5.1.2.1 Finite-Time Horizon LQ Problem; 5.1.2.2 Infinite-Time Horizon LQ Problem; 5.2 Two Person Zero-Sum Differential Games.
2.2 Differential Games and Their Solution Concepts2.2.1 Open-Loop Nash Equilibria; 2.2.2 Closed-Loop Nash Equilibria; 2.2.3 Feedback Nash Equilibria; 2.3 Stochastic Differential Games and Their Solutions; 2.3.1 The Model of Stochastic Differential Game; 2.3.2 The Solutions of Stochastic Differential Game; 3 Stochastic Differential Games of Continuous-Time Markov Jump Linear Systems; 3.1 Stochastic LQ Problem-Differential Game with One Player; 3.1.1 Finite-Time Horizon Case; 3.1.1.1 Problem Formulation; 3.1.1.2 Main Results; 3.1.2 Infinite-Time Horizon Case; 3.1.2.1 Problem Formulation.
3.1.2.2 Main Results3.2 Stochastic Nash Differential Games with Two Player; 3.2.1 Finite-Time Horizon Case; 3.2.1.1 Problem Formulation; 3.2.1.2 Main Results; 3.2.2 Infinite-Time Horizon Case; 3.2.2.1 Problem Formulation; 3.2.2.2 Main Results; 3.2.3 Two Person Zero-Sum Stochastic Differential Game; 3.2.3.1 Finite-Time Horizon Case; 3.2.3.2 Infinite-Time Horizon Case; 3.2.4 Numerical Example; 3.3 Stochastic Stackelberg Differential Game with Two Person; 3.3.1 Problem Formulation; 3.3.2 Main Results; 3.4 Summary; References.
4 Stochastic Differential Game of Discrete-Time Markov Jump Linear Systems4.1 Stochastic LQ Problem-Differential Game with One Person; 4.1.1 Finite-Time Horizon; 4.1.1.1 Problem Formulation; 4.1.1.2 Main Results; 4.1.2 Infinite-Time Horizon; 4.2 Stochastic Nash Differential Games with Two Person; 4.2.1 Finite-Time Horizon; 4.2.1.1 Problem Formulation; 4.2.1.2 Main Result; 4.2.2 Infinite-Time Horizon; 4.2.2.1 Problem Formulation; 4.2.2.2 Main Result; 4.2.3 Two Person Zero-Sum Stochastic Differential Games; 4.2.3.1 Finite Time Horizon; 4.2.3.2 Infinite-Time Horizon.
4.3 Stackelberg Differential Games with Two Person4.3.1 Finite-Time Horizon; 4.3.1.1 Problem Formulation; 4.3.1.2 Main Result; 4.3.2 Infinite-Time Horizon; 4.4 Summary; References; 5 Stochastic Differential Game of Stochastic Markov Jump Singular Systems; 5.1 Stochastic LQ Problems-Differential Games of One Player; 5.1.1 Preliminaries; 5.1.1.1 Stability of the Stochastic Markov Jump Singular Systems; 5.1.2 LQ Problem of Stochastic Markov Jump Singular Systems; 5.1.2.1 Finite-Time Horizon LQ Problem; 5.1.2.2 Infinite-Time Horizon LQ Problem; 5.2 Two Person Zero-Sum Differential Games.