A direct adaptive fuzzy sliding mode controller and its application

An approach of direct adaptive fuzzy sliding-mode control which combines the fuzzy control with the sliding-mode control, is proposed for the control of a class of unknown nonlinear dynamic systems. The control goal is to obtain a direct adaptive fuzzy sliding-mode control law and a constructive Lyapunov synthesis approach with respect to a class of nonlinear systems without the knowledge of uncertainties. For improving the approximate performance of the fuzzy system, the proposed approach in this study not only online updates the parameter values in the consequence fuzzy sets, but also updates the shape parameters of the membership functions of the prime fuzzy sets. The fuzzy control rules are updated through the online adaptive learning, which makes the output of fuzzy control to approximate to a sliding-mode equivalent control. The asymptotic stability of the overall system based on Lyapunov theory is proved. Some numerical simulation results show the efficiency of the proposed approach.