Policy iteration based cooperative linear quadratic differential games with unknown dynamics

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-02 DOI:10.1016/j.jfranklin.2024.107301

Jingbo Zhao, Zihao Zhao, Haiyi Yang, Chenchen Peng

{"title":"Policy iteration based cooperative linear quadratic differential games with unknown dynamics","authors":"Jingbo Zhao, Zihao Zhao, Haiyi Yang, Chenchen Peng","doi":"10.1016/j.jfranklin.2024.107301","DOIUrl":null,"url":null,"abstract":"<div><div>This article investigates the Pareto optimality of infinite horizon cooperative linear quadratic (LQ) differential games by policy iteration technique where the system dynamics are partially or completely unknown. Firstly, the policy iteration algorithm for the approximate solutions of the corresponding algebraic Riccati equation (ARE) without any prior knowledge of the matrix parameters of the dynamic system is derived by collecting the input and state information of each player. Secondly, when the presented specific rank condition is satisfied, the convergence of the proposed algorithm is rigorously demonstrated by recursion. Moreover, the weighting approach is employed to obtain the Pareto optimal strategy and the Pareto optimal solutions on the basis of the convex optimization theory. Finally, simulation results are reported to verify the feasibility and correctness of the proposed theoretical results.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"361 18","pages":"Article 107301"},"PeriodicalIF":3.7000,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003224007221","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 0

Abstract

This article investigates the Pareto optimality of infinite horizon cooperative linear quadratic (LQ) differential games by policy iteration technique where the system dynamics are partially or completely unknown. Firstly, the policy iteration algorithm for the approximate solutions of the corresponding algebraic Riccati equation (ARE) without any prior knowledge of the matrix parameters of the dynamic system is derived by collecting the input and state information of each player. Secondly, when the presented specific rank condition is satisfied, the convergence of the proposed algorithm is rigorously demonstrated by recursion. Moreover, the weighting approach is employed to obtain the Pareto optimal strategy and the Pareto optimal solutions on the basis of the convex optimization theory. Finally, simulation results are reported to verify the feasibility and correctness of the proposed theoretical results.

查看原文本刊更多论文

基于政策迭代的未知动态合作线性二次微分博弈

本文通过策略迭代技术研究了系统动态部分或完全未知的无限期合作线性二次微分（LQ）博弈的帕累托最优性。首先，通过收集各博弈方的输入和状态信息，在事先不知道动态系统矩阵参数的情况下，推导出相应代数里卡提方程（ARE）近似解的策略迭代算法。其次，在满足所提出的特定秩条件时，通过递归严格证明了所提出算法的收敛性。此外，在凸优化理论的基础上，采用加权法获得帕累托最优策略和帕累托最优解。最后，报告了仿真结果，以验证所提理论结果的可行性和正确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of The Franklin Institute-engineering and Applied Mathematics 工程技术-工程：电子与电气

CiteScore

7.30

自引率

14.60%

发文量

586

审稿时长

6.9 months

期刊介绍： The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.