Finite Time Tracker Design for Uncertain Nonlinear Fractional Order Systems

Abstract

This paper considers the problem of finitetime output tracking for a class of nonautonomous nonlinear fractionalorder (FO) systems in the presence of model uncertainties and external disturbances. The finitetime control methods indicate better properties in terms of robustness, disturbance rejection, and settling time. Thus, design of a robust nonsingular controller for finitetime output tracking of a timevarying reference signal is considered in this paper, and a novel FO nonsingular terminal sliding mode controller (TSMC) is designed, which can conquer the uncertainties and guarantees the finitetime convergence of the system output toward the desired timevarying reference signal. For this purpose, an appropriate nonsingular terminal sliding manifold is designed, where maintaining the system's states on this manifold leads to finitetime vanishing of error signal (i.e., ensures the finitetime occurrence of both reaching and sliding phases). Moreover, by tacking the fractional derivative of the sliding manifold, the convergence of system's trajectories into the terminal sliding manifold in a finite time is proven, and the convergence time is estimated. Finally, in order to verify the theoretical results, the proposed method is applied to an FO model of a horizontal platform system (FOHPS), and the computer simulations show the efficiency of the proposed method in finitetime output tracking.