Fuzzy Event-Triggered Integral Sliding Mode Control of Nonlinear Continuous-Time Systems

Abstract

This article investigates the design of an event-triggered-based integral sliding mode control (SMC) for a class of multiinput Takagi–Sugeno fuzzy model (TSFM)-based nonlinear systems with disturbance. Incorporating integral SMC scheme can be used along with the event-triggered control to deal with the simultaneous external disturbances and unnecessary waste of system resources. To further accommodate the characteristic of event-triggered integral SMC (ETISMC), two fuzzy integral switching surfaces are established. One is the triggered-state dependent switching surface which is proposed to obtain the ETISMC law. The other one is the conventional continuous-state dependent switching surface which is designed to ensure the robustness of the controlled system from the initial time instance. The proposed ETISMC is applicable for both single–input and multi–input, and despite the previous studies, a more reasonable ETISMC law is proposed with asynchronous premise variables. Based on Lyapunov function and adopting a decreasing time-varying triggering threshold in the event-triggered condition, the ultimately bounded stability of the closed-loop system is guaranteed. Sufficient conditions for the ultimate bounded of the trajectories of the system states are formulated in terms of new offline linear matrix inequalities. Moreover, the positive lower bound of the internal execution is ensured, which means that there is no Zeno phenomenon. To demonstrate the superiority of the proposed technique, the suggested ETISMC is applied to a two-degree freedom helicopter system and the simulation results verify the validity of the proposed control strategy.