关键词: 广义随机系统； Nash微分博弈； Riccati方程； 随机H₂/H_∞控制

Abstract:

A class of Nash differential games of continuoustime singular stochastic affine systems with multiple decision makers is investigated. After establishing some concepts of the stability for stochastic singular systems, the condition of the stability is presented by means of a linear matrix inequality. Then, by utilizing Riccati equation approach, the existence conditions of equilibrium strategy set in finite horizon and infinite horizon are obtained by means of a set of cross coupled differential Riccati equations or a set of cross coupled algebraic Riccati equations, respectively. And explicit expressions of the optimal feedback controls and optimal cost function are given. In the end, the obtained results are used to deal with the stochastic H₂/H_∞ control problem in the fields of modern robust control theory, and the existence conditions of robust control strategies and explicit expressions are obtained.

Key words: singular stochastic systems; Nash differential games; Riccati equation; stochastic H₂/H_∞control