Adaptive fuzzy fractional-order fast terminal sliding mode control for a class of uncertain nonlinear systems

The paper introduces a novel adaptive fuzzy fractional-order (FO) fast terminal sliding mode control procedure for a class of nonlinear systems in the presence of uncertainties and external disturbances. For this purpose, firstly, using fractional calculus, a new FO nonlinear sliding surface is proposed and then, the corresponding FO fast terminal sliding mode controller (FOFTSMC) is designed to satisfy the sliding condition in finite time. Next, to eliminate the chattering phenomenon, a fuzzy system is constructed to design a continuous switching control law. The finite-time stability of the proposed adaptive fuzzy FOFTSMC (AFFOFTSMC) is proved using the concept of Lyapunov stability theorem. Finally, to illustrate the effectiveness of the proposed AFFOFTSMC, three examples are given as case studies. The numerical simulation results confirm the superiority of the proposed controller, which are the better robust performance, faster convergence, finite-time stability of the closed-loop control system, and a chattering free control effort compared to other mentioned control methods.