An Efficient Impulsive Adaptive Dynamic Programming Algorithm for Stochastic Systems

In this study, a novel general impulsive transition matrix is defined, which can reveal the transition dynamics and probability distribution evolution patterns for all system states between two impulsive ``events,'' instead of two regular time indexes. Based on this general matrix, the policy iteration-based impulsive adaptive dynamic programming (IADP) algorithm along with its variant, which is a more efficient IADP (EIADP) algorithm, are developed in order to solve the optimal impulsive control problems of discrete stochastic systems. Through analyzing the monotonicity, stability, and convergency properties of the obtained iterative value functions and control laws, it is proved that the IADP and EIADP algorithms both converge to the optimal impulsive performance index function. By dividing the whole impulsive policy into smaller pieces, the proposed EIADP algorithm updates the iterative policies in a ``piece-by-piece'' manner according to the actual hardware constraints. This feature of the EIADP method enables these ADP-based algorithms to be fully optimized to run on all ``sizes'' of computing devices including the ones with low memory spaces. A simulation experiment is conducted to validate the effectiveness of the present methods.