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∞ -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.
Keywords :
H∞ control; H∞ optimisation; autoregressive moving average processes; discrete systems; fuzzy control; fuzzy systems; nonlinear control systems; robust control; sensitivity analysis; stochastic systems; transfer functions; variable structure systems; ARMAX model; H∞ norm space; approximation error; dead-beat to switching surface; discrete variable structure control; fuzzy linear-model-based robust control; fuzzy pulse transfer function; fuzzy switching control; nonlinear stochastic system; nonlinear time-varying uncertainties; sensitivity minimization; stochastic fuzzy-model system; weighted combination of subsystems; weighted sensitivity function; Approximation error; Fuzzy control; Fuzzy systems; Nonlinear dynamical systems; Robust control; Stochastic resonance; Stochastic systems; Time varying systems; Uncertainty; White noise;
