Adaptive Fuzzy DSC Design of Strict-Feedback Fractional-Order Nonlinear Systems

Abstract

This paper proposes an adaptive fuzzy backstepping dynamic surface control (DSC) method for a class of single-input-single-output (SISO) strict-feedback fractional-order nonlinear systems with uncertain nonlinearities. Fuzzy logic systems (FLSs) are employed for approximating the unknown nonlinear functions. A novel nonlinear fractional-order filter with an auxiliary function is designed to avoid the issue of explosion of complexity inherent in the backstepping procedure. Meanwhile, the stability of the closed-loop system is proved by use of the fractional-order Lyapunov function stability criterion. Finally, a Chua’s circuit simulation example is given to validate the effectiveness of our proposed control strategy.