Mixed ℋ2/ℋ∞ fault-tolerant control for nonlinear stochastic systems: The finite-horizon case

This paper deals with the fault-tolerant control problem for a class of nonlinear stochastic time-varying system with actuator failures. Both ℋ₂ and ℋ_∞ performance requirements are taken into consideration. The proposed actuator failure model is quite general and cover several frequently seen actuator failure phenomena as special cases. The stochastic nonlinearities are quite general and could stand for several nonlinear systems. It is the purpose of this paper to find equilibrium strategies of a two-player Nash game, and meanwhile both ℋ₂ and ℋ_∞ performances are achieved via proposed state feedback control scheme which is characterized by the solution to a set of coupled matrix equations. The feedback gains can be solved recursively backward in k. A numerical computing algorithm is presented, and then a simulation example is given to illustrate the effectiveness and applicability of the proposed algorithm.