Barrier Function Adaptive Event-Triggered Sliding Mode Control for Nonlinear Systems

The paper presents a Barrier Function Adaptive Event-Triggered (ET) Sliding Mode Controller (SMC) for a class of nonlinear systems with matched disturbances. The proposed approach integrates barrier-function-based gain adaptation into the event-triggered sliding mode framework while preserving the original triggering mechanism. Two adaptive barrier functions, namely the Positive Barrier Function and the Positive Semi-Barrier Function, are employed to continuously adjust the switching gain according to the evolution of the sliding variable. Stability of the closed-loop system is established using Lyapunov and input-to-state stability analysis, and a positive lower bound on the inter-event time is derived to exclude Zeno behavior. Theoretical results demonstrate that adaptive gain scheduling enlarges the guaranteed inter-event time compared with conventional ET-SMC. The proposed controller is experimentally validated on an air-levitation system and compared with conventional time-triggered SMC and fixed-gain ET-SMC. Experimental results confirm preserved robustness and disturbance rejection while significantly reducing controller updates and increasing the inter-event time, demonstrating the effectiveness of the proposed adaptive event-triggered strategy.