四川大学学报（自然科学版）2025，Vol.62Issue(3)：569-583,15.DOI:10.19907/j.0490-6756.240092
基于输出反馈的随机自适应线性二次零和博弈
Stochastic adaptive linear quadratic zero-sum games via output feedback
摘要
Abstract
In this paper,the adaptive zero-sum game problem for discrete-time linear system with both pro-cess and measurement noises and unknown coefficient matrices is studied under the quadratic ergodic cost function.To address this issue,an adaptive output feedback control strategy is designed,which only relies on the input and output data of the system without requiring the coefficient matrices of the system.Firstly,com-bined with the weighted least squares(WLS)method,random regularization and diminishing excitation tech-niques,each player uses the input and output data of the system to estimate the unknown coefficient matrices and system state.Then,based on these estimates and the certainty equivalence principle,each player designs their respective adaptive output feedback control strategy.Under some certain conditions,it is proved that the designed adaptive output feedback control strategies constitute saddle-point strategies and can make the closed-loop game system globally stable.Finally,a numerical simulation is given to verify the effectiveness of the designed adaptive control strategies.关键词
输出反馈/零和博弈/加权最小二乘法/衰减激励/鞍点策略Key words
Output feedback/Zero-sum game/WLS/Diminishing excitation/Saddle-point strategy分类
数理科学引用本文复制引用
田秀芹,杨雪,刘淑君..基于输出反馈的随机自适应线性二次零和博弈[J].四川大学学报（自然科学版）,2025,62(3):569-583,15.基金项目
四川省自然科学基金(2024NSFSC0437) （2024NSFSC0437）
