Nash equilibrium precision controllability and linear quadratic optimal control for stochastic switched systems

In this paper, a class of stochastic switched systems based on non-cooperative dynamic games has been considered, and the dynamic game involves one leader and multiple followers. From the viewpoint of the forward and backward stochastic differential equations(FBSDE), a sufficient and necessary condition characterizing the Nash Equilibrium stochastic exact controllability and algebraic criteria of the system are obtained, it is interesting that If the stochastic system degenerate to deterministic systems, the condition for stochastic exact controllability becomes the counterpart for complete controllability of linear deterministic control systems.