Finite horizon H∞ control for stochastic systems with multiple decision makers

This paper investigates the finite horizon H_∞ control problem for a class of nonlinear stochastic systems with multiple decision makers. First, it is shown that the H_∞ controllers for the decision makers can be obtained by solving a dynamic Nash game problem. In order to find the H_∞ controllers, necessary conditions for the existence of Nash equilibrium in the worst case disturbance, which consist of cross-coupled forward-backward stochastic differential equations (CFBSDEs), are derived by using stochastic maximum principle. Second, a four step scheme is adopted to develop a computational algorithm to solve the CFBSDEs. A simple practical example is solved to show the validity of the proposed method.