Adaptive Fuzzy Backstepping Dynamic Surface Control of Strict-Feedback Fractional-Order Uncertain Nonlinear Systems

This paper presents a novel adaptive fuzzy backstepping dynamic surface control (DSC) scheme for a class of single-input single-output strict-feedback fractional-order uncertain nonlinear systems. The controlled systems contain unknown nonlinear functions and unknown external disturbances. Fuzzy logic systems are employed for approximating the unknown nonlinear functions. Further, an auxiliary function is introduced into the control function to simultaneously compensate the unknown external disturbance and the approximation error caused by fuzzy approximation, which erases the possible chattering phenomenon in the existing results. Meanwhile, a new DSC method based on the fractional-order filter is proposed to avoid the issue of explosion of complexity inherent in the backstepping procedure, which releases the limitation that the fractional-order derivative of the intermediate control function needs to be completly known in the existing references. Under certain assumptions, the stability of the closed-loop system is proved by using the fractional-order Lyapunov function stability criterion. Finally, contrastive simulation results are provided to validate the effectiveness of our proposed control strategy.