Backstepping nonlinear control using nonlinear parametric fuzzy systems

Based on nonlinear parametric fuzzy systems, an adaptive backstepping controller is proposed for a class of strict-feedback nonlinear systems. The nonlinear parametric fuzzy systems are capable of automatically learning their membership functions and tuning their weightings. Since the adjustable parameters of the membership functions nonlinearly appear in the fuzzy systems, the adaptive laws are derived by estimating the derivative of the fuzzy systems. Moreover, the stability of the closed-loop system is analyzed by means of Lyapunov theory, and some tracking performance is guaranteed. Finally, two examples are provided to demonstrate the effectiveness and applicability of the proposed scheme.