Event-triggered adaptive fuzzy tracking control for a class of fractional-order uncertain nonlinear systems with external disturbance

Abstract

In this paper, we are dedicated to addressing the event-triggered adaptive fuzzy tracking control problem for a class of fractional-order nonlinear systems (FONSs) with uncertainty and external disturbance. A novel condition is presented for estimating the fractional derivative of event-triggered strategy measurement error signal. To avoid the “expansion of complexity” problem caused by repeatedly solving the fractional derivatives of the virtual control signals in the backstepping method, an event-triggered-based adaptive fuzzy controller is constructed by taking advantage of the fractional dynamic surface control (DSC) scheme and fractional Lyapunov direct method. The designed controller can not only guarantee the tracking error finally converges to a small neighborhood around the origin, but also ensure all signals included in closed-loop FONSs are semiglobally uniformly ultimate bounded (SUUB) and the Zeno behavior is favorably avoided. In addition, the fuzzy logic systems (FLSs) tend to be applied in estimating the unknown nonlinear function, and an auxiliary function is also adopted to compensate for the approximation error of FLSs and the external disturbance. Finally, a numerical example indicates that the event-triggered adaptive fuzzy controller designed in this paper for FONSs is feasible and effective.