Reliable mixed ℋ2/ℋ∞ control for stochastic time-varying systems against actuator failures

This paper is concerned with the reliable control problem for stochastic time-varying system subject to possible actuator failures while satisfying both ℋ₂ and ℋ_∞ performance requirements simultaneously. The proposed actuator failure model is quite general and is able to illustrate several actuator failure phenomena frequently seen in literature. The purpose of this problem is, via state feedback, to find equilibrium strategies of a two-player Nash game, and meanwhile both ℋ₂ and ℋ_∞ performances are achieved. The resulting state feedback controller is characterized by the solution to a set of coupled matrix equations, by which 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.