{"title":"Distributed Nash Equilibrium Seeking for Nonlinear Players With Input Delay","authors":"Zhaoming Sheng;Qian Ma","doi":"10.1109/TSIPN.2024.3451979","DOIUrl":null,"url":null,"abstract":"This paper studies the distributed Nash equilibrium seeking problem for players subject to unknown nonlinear dynamics and input delay. By designing a distributed estimator for each player to estimate other players' decisions and embedding an auxiliary variable to compensate for the influence of unknown nonlinearities, the distributed Nash equilibrium seeking algorithms are obtained for first-, second-, and high-order nonlinear players, respectively. With the help of the Lyapunov stability theory and Lyapunov-Krasovskii functional approach, the maximum allowable input delay is determined and the global asymptotic convergence of players' decisions to the Nash equilibrium is proved. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed methods.","PeriodicalId":56268,"journal":{"name":"IEEE Transactions on Signal and Information Processing over Networks","volume":"10 ","pages":"679-689"},"PeriodicalIF":3.0000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Signal and Information Processing over Networks","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10659233/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
This paper studies the distributed Nash equilibrium seeking problem for players subject to unknown nonlinear dynamics and input delay. By designing a distributed estimator for each player to estimate other players' decisions and embedding an auxiliary variable to compensate for the influence of unknown nonlinearities, the distributed Nash equilibrium seeking algorithms are obtained for first-, second-, and high-order nonlinear players, respectively. With the help of the Lyapunov stability theory and Lyapunov-Krasovskii functional approach, the maximum allowable input delay is determined and the global asymptotic convergence of players' decisions to the Nash equilibrium is proved. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed methods.
期刊介绍：
The IEEE Transactions on Signal and Information Processing over Networks publishes high-quality papers that extend the classical notions of processing of signals defined over vector spaces (e.g. time and space) to processing of signals and information (data) defined over networks, potentially dynamically varying. In signal processing over networks, the topology of the network may define structural relationships in the data, or may constrain processing of the data. Topics include distributed algorithms for filtering, detection, estimation, adaptation and learning, model selection, data fusion, and diffusion or evolution of information over such networks, and applications of distributed signal processing.
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