Command Filter-Based Adaptive Fuzzy Finite-Time Tracking Control for Uncertain Fractional-Order Nonlinear Systems

Abstract

In this article, we focus on the issue of adaptive fuzzy finite-time tracking control for a class of uncertain fractional-order nonlinear systems with external disturbance. A new finite-time fractional-order command filtered implementation scheme is presented for the adaptive backstepping method. In the command filtered implementation approach, analytical computation of the fractional derivatives of the stabilizing functions is not necessary. Therefore, the controller and adaptive law of the systems are easier to derive and implement. Based on the proposed command filter, adaptive backstepping technique, and fractional Lyapunov’s direct method, a novel adaptive fuzzy finite-time controller is designed, which can guarantee that the tracking error converges to a small neighborhood of the origin in finite time, and other signals of the closed-loop systems are semiglobal uniform ultimate bounded. In the design process of the controller, fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions, and an auxiliary function is adopted to compensate for the unknown external disturbance and approximation errors of FLSs. Finally, a simulation example is given to show the effectiveness and availability of the proposed control strategy.