Minimax Q-learning design for H_(∞) control of linear discrete-time systems  

作　　者：Xinxing LI Lele XI Wenzhong ZHA Zhihong PENG 

机构地区：[1]Information Science Academy,China Electronics Technology Group Corporation,Beijing 100086,China [2]School of Automation,Beijing Institute of Technology,Beijing 100081,China [3]Peng Cheng Laboratory,Shenzhen 518052,China

出　　处：《Frontiers of Information Technology & Electronic Engineering》2022年第3期438-451,共14页信息与电子工程前沿（英文版）

基　　金：supported by the National Natural Science Foundation of China (No. U1613225)。

摘　　要：The H_(∞)control method is an effective approach for attenuating the effect of disturbances on practical systems, but it is difficult to obtain the H_(∞)controller due to the nonlinear Hamilton-Jacobi-Isaacs equation, even for linear systems. This study deals with the design of an H_(∞)controller for linear discrete-time systems. To solve the related game algebraic Riccati equation(GARE), a novel model-free minimax Q-learning method is developed, on the basis of an offline policy iteration algorithm, which is shown to be Newton’s method for solving the GARE. The proposed minimax Q-learning method, which employs off-policy reinforcement learning, learns the optimal control policies for the controller and the disturbance online, using only the state samples generated by the implemented behavior policies. Different from existing Q-learning methods, a novel gradient-based policy improvement scheme is proposed. We prove that the minimax Q-learning method converges to the saddle solution under initially admissible control policies and an appropriate positive learning rate, provided that certain persistence of excitation(PE)conditions are satisfied. In addition, the PE conditions can be easily met by choosing appropriate behavior policies containing certain excitation noises, without causing any excitation noise bias. In the simulation study, we apply the proposed minimax Q-learning method to design an H_(∞)load-frequency controller for an electrical power system generator that suffers from load disturbance, and the simulation results indicate that the obtained H_(∞)load-frequency controller has good disturbance rejection performance.

关 键 词：H_(∞)control Zero-sum dynamic game Reinforcement learning Adaptive dynamic programming Minimax Q-learning Policy iteration 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]