Adaptive Fuzzy Dynamic Surface Control for A Class of Fractional-Order Uncertain Nonlinear Systems

This paper is devoted to addressing the issue of adaptive fuzzy control for single-input single-output (SISO) fractional-order nonlinear systems with uncertainty. In order to avoid the “explosion of terms” caused by solving the fractional derivative of virtual signal, a new fractional-order dynamic surface control (DSC) method is proposed for fractional-order systems. Based on backstepping technique and Lyapunov direct method for fractional derivatives, the stability of closed-loop system is proved, which can ensure that the tracking error can converge to a small region. Finally, a simulation example is provided to reveal the effectiveness of the proposed control scheme.