Self-Triggered Prescribed-Time Impulsive Control for Nonlinear Systems

This article presents a new design of self-triggered impulsive control (STIC) for prescribed-time stability (PTS) of nonlinear systems. A prescribed-time convergent function is proposed to determine the impulsive control strength together with the information of the impulsive interval. Different from previous impulsive control strategies, the impulsive control with designable strength is implemented under a non-Zeno self-triggering mechanism (STM) with enforced bounded execution times and the triggering times established by a comparison system. The involvement of the upper bound of the impulsive interval in both control strength and STM not only renders the closed-loop prescribed-time stable but also ensures decreasing impulsive strengths as the time approaches the prescribed time. The validity of the proposed STIC scheme is verified by the application to prescribed-time synchronization of reaction-diffusion neural networks (RDNNs) and numerical examples.