Optimal Control of Stochastic System with Markovian Jumping and Multiplicative Noises

An optimization problem for a stochastic system of N players is presented. An optimal Pareto controller of the stochastic system with Markovian jumping and multiplicative white noises is designed in infinite time horizon. The optimal Pareto solution is obtained by using the generalized Lyapunov equation approach and solving stochastic generalized Riccati algebraic equations (SGRAEs). It is proved that the controller is a stabilizing feedback control and the solution of SGRAEs is minimal associated with the optimal control.