Fuzzy Adaptive Backstepping Control For Uncertain Nonlinear Stochastic System

This paper investigated the stabilization problem for a class of uncertain nonlinearstochastic systems mainly by using the stochastic stabilization theory, adaptive fuzzyBackstepping technique. The main contributions of the paper are as following(1) An adaptive fuzzy output feedback control approach is investigated for a class ofSISO stochastic nonlinear strict-feedback systems without the requirement of the statesmeasurement. First a fuzzy state observer is designed to estimate the unmeasured states. Thenby introducing stochastic small-gain theory to handle the problem of unmodeled dynamics,and by using Backstepping technique, a fuzzy adaptive controller is constructed. Furthermore,it is proved that the proposed control approach can guarantee that the closed-loop system isinput-state-practically stability (ISpS) in probability based on the Lyapunov function theory,and the observer errors and the output of the system converge to a small neighborhood of theorigin by appropriate choice of the design parameters. Simulation results are included toindicate that the proposed adaptive fuzzy control approach has a satisfactory controlperformance.(2) Based on the above contribution, and assume that the control input contains theunknown dead-zone. Then, it is proved that the proposed control approach can guarantee thatthe closed-loop system is ISpS in probability based on the Lyapunov function theory, and theobserver errors and the output of the system converge to a small neighborhood of the originby appropriate choice of the design parameters. Simulation results are included to indicatethat the proposed adaptive fuzzy control approach has a satisfactory control performance.(3) An adaptive fuzzy output feedback control approach is investigated for a class ofstochastic nonlinear strict-feedback systems with unknown control direction. The problem ofunknown control direction is handled by introducing the Nussbaum technique. By combiningthe backstepping design technique with the changing supply function approach, a newadaptive fuzzy controller is constructed. In addition, it is proved that the proposed controlapproach can guarantee that the closed-loop system is ISpS in probability based on theLyapunov function theory, and the observer errors and the output of the system converge to asmall neighborhood of the origin by appropriate choice of the design parameters. Simulationresults are included to indicate that the proposed adaptive fuzzy control approach has asatisfactory control performance.(4) An adaptive decentralized fuzzy control approach is investigated for a class oflarge-scale stochastic nonlinear systems with unknown dead-zones. By combining thebackstepping design technique with the dynamical signal approach, a new adaptive fuzzydecentralized controller is constructed. In addition, it is proved that the proposeddecentralized control approach can guarantee that the closed-loop system is ISpS inprobability based on the Lyapunov function theory, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the designparameters. Simulation results are included to indicate that the proposed adaptivedecentralized fuzzy control approach has a satisfactory control performance.(5) An adaptive decentralized fuzzy control approach is investigated for a class oflarge-scale stochastic nonlinear systems with unmodeled dynamics. By combining thebackstepping design technique with the changing supply function approach, a new adaptivedecentralized fuzzy controller is constructed. In addition, it is proved that the proposeddecentralized control approach can guarantee that the closed-loop system is ISpS inprobability based on the Lyapunov function theory, and the observer errors and the output ofthe system converge to a small neighborhood of the origin by appropriate choice of the designparameters. Simulation results are included to indicate that the proposed adaptivedecentralized fuzzy control approach has a satisfactory control performance.