{"title":"有界控制输入的离散时间系统中四元博弈的分布式纳什均衡寻求","authors":"","doi":"10.1016/j.jfranklin.2024.107226","DOIUrl":null,"url":null,"abstract":"<div><p>This paper considers the distributed Nash equilibrium seeking problem for quadratic games in discrete-time systems with bounded control inputs. First, a saturation gradient algorithm is proposed to seek the Nash equilibrium without considering the limitations of communication. Then the case that players can only communicate with their neighbors is considered, a distributed Nash equilibrium seeking algorithm is designed where a consensus protocol is adapted for information sharing. In the proposed distributed algorithm, each player has an estimate on others’ actions and the consensus of players’ estimates is achieved. By Lyapunov stability theory for discrete-time systems, it is shown that the Nash equilibrium of the game is globally asymptotically stable under certain conditions. Moreover, distributed Nash equilibrium seeking problem in hybrid systems with bounded control inputs is solved. Finally, two numerical examples are presented to verify the effectiveness of the proposed algorithms.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Distributed Nash equilibrium seeking for quadratic games in discrete-time systems with bounded control inputs\",\"authors\":\"\",\"doi\":\"10.1016/j.jfranklin.2024.107226\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper considers the distributed Nash equilibrium seeking problem for quadratic games in discrete-time systems with bounded control inputs. First, a saturation gradient algorithm is proposed to seek the Nash equilibrium without considering the limitations of communication. Then the case that players can only communicate with their neighbors is considered, a distributed Nash equilibrium seeking algorithm is designed where a consensus protocol is adapted for information sharing. In the proposed distributed algorithm, each player has an estimate on others’ actions and the consensus of players’ estimates is achieved. By Lyapunov stability theory for discrete-time systems, it is shown that the Nash equilibrium of the game is globally asymptotically stable under certain conditions. Moreover, distributed Nash equilibrium seeking problem in hybrid systems with bounded control inputs is solved. Finally, two numerical examples are presented to verify the effectiveness of the proposed algorithms.</p></div>\",\"PeriodicalId\":17283,\"journal\":{\"name\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-08-30\",\"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/S0016003224006471\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003224006471","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}
Distributed Nash equilibrium seeking for quadratic games in discrete-time systems with bounded control inputs
This paper considers the distributed Nash equilibrium seeking problem for quadratic games in discrete-time systems with bounded control inputs. First, a saturation gradient algorithm is proposed to seek the Nash equilibrium without considering the limitations of communication. Then the case that players can only communicate with their neighbors is considered, a distributed Nash equilibrium seeking algorithm is designed where a consensus protocol is adapted for information sharing. In the proposed distributed algorithm, each player has an estimate on others’ actions and the consensus of players’ estimates is achieved. By Lyapunov stability theory for discrete-time systems, it is shown that the Nash equilibrium of the game is globally asymptotically stable under certain conditions. Moreover, distributed Nash equilibrium seeking problem in hybrid systems with bounded control inputs is solved. Finally, two numerical examples are presented to verify the effectiveness of the proposed algorithms.
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.