Adaptive Fuzzy Sliding Mode Control for a Class of Uncertain Nonaffine Nonlinear Strict-Feedback Systems

In this paper, an adaptive fuzzy sliding mode scheme is proposed for a class of single-input, single-output(SISO) unknown uncertain nonaffine nonlinear systems in strict-feedback form. In this scheme, the backstepping algorithm is used to obtain the virtual controllers. The real control law is designed by using sliding mode approach. The both matched and mismatched unknown uncertainties are counteracted by using adaptive robust terms. The unknown nonlinear functions are approximated by employing adaptive fuzzy logic systems. The adaptation laws of the adjustable parameters are deduced from the stability analysis of the closed-loop system in the sense of Lyapunov. The derived adaptive fuzzy sliding mode control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the tracking error to a very small neighborhood of the origin. Numerical simulation results are provided to show the effectiveness of the proposed control scheme.