Adaptive Multi-Step Evaluation Design With Stability Guarantee for Discrete-Time Optimal Learning Control  

作　　者：Ding Wang Jiangyu Wang Mingming Zhao Peng Xin Junfei Qiao 

机构地区：[1]IEEE [2]Faculty of Information Technology,the Beijing Key Laboratory of Computational Intelligence and Intelligent System,the Beijing Laboratory of Smart Environmental Protection,and the Beijing Institute of Artificial Intelligence,Beijing University of Technology,Beijing 100124,China

出　　处：《IEEE/CAA Journal of Automatica Sinica》2023年第9期1797-1809,共13页自动化学报（英文版）

基　　金：the National Key Research and Development Program of China(2021ZD0112302);the National Natural Science Foundation of China(62222301,61890930-5,62021003);the Beijing Natural Science Foundation(JQ19013).

摘　　要：This paper is concerned with a novel integrated multi-step heuristic dynamic programming(MsHDP)algorithm for solving optimal control problems.It is shown that,initialized by the zero cost function,MsHDP can converge to the optimal solution of the Hamilton-Jacobi-Bellman(HJB)equation.Then,the stability of the system is analyzed using control policies generated by MsHDP.Also,a general stability criterion is designed to determine the admissibility of the current control policy.That is,the criterion is applicable not only to traditional value iteration and policy iteration but also to MsHDP.Further,based on the convergence and the stability criterion,the integrated MsHDP algorithm using immature control policies is developed to accelerate learning efficiency greatly.Besides,actor-critic is utilized to implement the integrated MsHDP scheme,where neural networks are used to evaluate and improve the iterative policy as the parameter architecture.Finally,two simulation examples are given to demonstrate that the learning effectiveness of the integrated MsHDP scheme surpasses those of other fixed or integrated methods.

关 键 词：Adaptive critic artificial neural networks Hamilton-Jacobi-Bellman(HJB)equation multi-step heuristic dynamic programming multi-step reinforcement learning optimal control 

分 类 号：O232[理学—运筹学与控制论] TP18[理学—数学]