Fuzzy linear-model-based robust control for a class of nonlinear stochastic systems

Abstract

In this paper, a nonlinear stochastic system (NSS) is approximated by weighted combination of N subsystems, which are described by ARMAX model (autoregressive moving-average model with exogenous input). The approximation error between the NSS and the stochastic fuzzy-model system (SFMS) is represented by nonlinear time-varying uncertainties (NTVU) in every subsystem. In the beginning, a dead-beat to the switching surface for every nominal subsystem is designed. The total disturbance of the ith subsystem is caused by the white noise, the approximation error of SFMS, and the interaction dynamics resulting from the other subsystems. In general, it is not small. Then the H/sup /spl infin// -norm of the weighted sensitivity function between the switching surface and the total disturbance is minimized. For obtaining a better performance, a fuzzy switching control is also designed. Finally, the simulations are carried out to confirm the validity of the proposed control.