Event-Triggered Impulsive Control for Nonlinear Systems: A Q-Learning-Enhanced Memory-Based Method

An intelligent memory-based event-triggered impulsive control (METIC) scheme is proposed to address the stabilization problem for a class of nonlinear systems while accounting for exponential convergence, dynamic performance, and control frequency. The contribution of the scheme is the incorporation of weighted historical data into the triggering condition, using both fixed thresholds and adaptive thresholds based on Q-learning. By utilizing the system states at the two most recent triggering instants to construct the triggering condition, several exponential stability criteria are first established via an iterative approach. Then, in the general case in which additional historical states are included, a comparison system approach is employed to derive new stability conditions. Furthermore, to adaptively tune the event-triggering thresholds and improve system performance, a Q-learning-based optimization algorithm is developed, and a set of easily verifiable stability conditions is derived within the framework of switched system theory. For both fixed-threshold and adaptive-threshold cases, Zeno behavior is rigorously excluded through theoretical analysis. Finally, comparative simulation results are presented to demonstrate the effectiveness of the proposed method.