An Efficient Impulsive Adaptive Dynamic Programming Algorithm for Stochastic Systems
定义了通用脉冲转移矩阵，提出脉冲自适应动态规划算法及其高效变体，用于求解离散随机系统的最优脉冲控制问题，并证明收敛性。
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.