Adaptive fuzzy prescribed performance controller design for a class of uncertain fractional-order nonlinear systems with external disturbances.

A fractional-order adaptive fuzzy controller, capable of guaranteeing prescribed performance, is designed for a class of uncertain fractional-order nonlinear systems with external disturbances in this paper. With respect to the prescribed performance control, we mean that the system variables converge to an arbitrary small region of the origin with convergence rate no less than a certain prescribed function. Fuzzy logic system is utilized to approximate an unknown nonlinear function which contains fractional-order terms. Based on the Lyapunov stability criterion, a fractional-order adaptive fuzzy sliding mode controller, which can guarantee the stability of the closed-loop system as well as the prescribed performance, is constructed. Finally, simulation results are given to confirm our results.