Abstract:

 The maximum principle for nonzero-sum stochastic differential games was applied to solve the stochastic H2／H∞ control problem with (x,u,v)-dependent noise. It is shown that the existence of a unique solution to the control problem is equivalent to the corresponding uncontrolled perturbed system to have L2-gain less than or equal to γ and the resulting solution is characterized by the solution of an uncontrolled forward backward stochastic differential equation (FBSDE).

Key words: the maximum principle; stochastic H2／H∞ control; forward backward stochastic differential equation (FBSDE); Riccati equation