Variance-Constrained Multi-Objective Stochastic Control and Filtering

Chapter 14Mixed H₂/H_∞ Control with Actuator Failures: the Finite-Horizon Case

This chapter deals with the fault-tolerant control problem for a class of nonlinear stochastic time-varying systems with actuator failures. Both H₂ and H_∞ performance requirements are taken into consideration. The proposed actuator failure model is quite general and could cover several frequently seen actuator failure phenomena as special cases. The stochastic nonlinearities are quite general and could represent several types of nonlinear systems. It is the purpose of this chapter to find equilibrium strategies of a two-player Nash game, and meanwhile both H₂ and H_∞ performances are achieved via a 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.

The rest of the chapter is arranged as follows: Section 14.1 formulates the mixed H₂/H_∞ control problem for the nonlinear stochastic time-varying systems with actuator failures. In Section 14.2, the H_∞ performance is analyzed in terms of the Riccati equation method. Section 14.3 gives the methodology to solve the addressed multi-objective problem and outlines the computational algorithm to recursively obtain the required parameters. A numerical example is presented in Section ...