Optimal Event-Triggered Impulsive Control for Stochastic Systems using ADP

In this paper, a novel general-event-based impulsive transition matrix (GITM) is constructed, which can reveal the probability distribution evolution patterns for all system states across the impulsive instants, instead of the regular time indexes. Based on the GITM, the event-triggered impulsive adaptive dynamic programming (ETIADP) algorithm and a high-efficiency event-triggered impulsive adaptive dynamic programming (HEIADP) algorithm are developed. It is shown that the proposed methods can solve the optimal impulsive control problems of discrete stochastic systems, while reducing the computational and communication burden caused by updating the controller periodically. Convergency analysis is provided to show that both the ETIADP and HEIADP algorithms can converge to the optimal impulsive performance index function. The proposed HEIADP algorithm updates policies and value functions partially at each iteration step according to actual hardware constraints, reducing the memory consumption of the ADP implementation. The simulation experiment is conducted to validate the effectiveness of the developed methods.