Adaptive fuzzy backstepping control for a class of uncertain nonlinear strict-feedback systems based on dynamic surface control approach

Abstract

Abstract In this paper, a singularity-free adaptive fuzzy backstepping control\xa0(AFBC) scheme is presented for uncertain nonlinear SISO systems with triangular structure by using dynamic surface control\xa0(DSC) design technique. As the intelligent approximator, fuzzy logic systems are employed to approximate the continuous nonlinear unknown functions in the uncertain systems. By utilizing DSC design technique into AFBC design framework, the proposed intelligent-based adaptive control system can overcome the problem of “explosion of complexity” inherent in the backstepping design method. Moreover, the further benefits of the proposed intelligent-based adaptive control method are that the control singularity problem is completely prevented and the upper bounds of the time differential of the gain functions are no longer needed during the control scheme design. Based on the backstepping technique, it can be proven that the closed-loop system is stable in the sense that all the variables are guaranteed to be bounded. The simulation examples demonstrate and validate the effectiveness of the proposed intelligent-based adaptive control method.