Adaptive fuzzy sliding mode control with unknown virtual control coefficients and perturbed uncertainties

The problem of adaptive fuzzy sliding mode control for a class of nonlinear systems with unknown virtual control coefficients and perturbed uncertainties is discussed in this paper. By introducing boundary layer, and combining backstepping technique with direct adaptive control, a novel scheme of adaptive fuzzy control is proposed. In order to reduce the modeling error effect and improve the control performance of the closed-loop system, the adaptive compensation term of the approximation error and disturbance is introduced within virtual control and control law design. By Lyapunov method, the closed-loop control system is shown to be uniformly ultimately bounded, and tracking error asymptotically converges to an arbitrary given accuracy.