Event-Triggered Practical Predefined-Time Fault-Tolerant Synchronization of Second-Order Chaotic Systems

This study addresses the synchronization problem of second-order chaotic systems subject to parameter uncertainties, external disturbances, and actuator faults, and proposes a predefined-time nonsingular terminal sliding mode control (NTSMC) strategy. A nonsingular terminal sliding surface is designed so that the convergence time can be prescribed in advance. A time-varying barrier-function-based adaptive gain is developed to increase the robust gain as the sliding variable approaches the barrier boundary. The proposed strategy does not require prior knowledge of the disturbance upper bound, thereby avoiding control-gain overestimation associated with conventional fixed-gain or adaptive-gain approaches. In addition, a periodic event-triggering mechanism (ETM) is designed to transmit a new command only when the deviation of the nominal compensation command from its held value exceeds a threshold, thereby reducing the communication burden. The stability of the closed-loop system is established using Lyapunov theory. Finally, several simulation experiments demonstrate the feasibility and superior performance of the proposed scheme.