Adaptive fuzzy control for strict-feedback nonlinear systems

The problem of direct adaptive fuzzy control for a class of strict-feedback uncertain systems is discussed in this paper. Based on the principle of sliding mode control and the approximation capability of fuzzy systems, and by introducing modulation function, a novel scheme of direct adaptive fuzzy control is proposed. By utilizing backstepping technique, each virtual control and the adaptation law of the adjustable parameters in the fuzzy systems as well as the super bounds of the approximation errors are determined in turn. Finally, the control law is determined. 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 is introduced. 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.