{"title":"希尔伯特空间中追逐-逃避微分对策问题的对策值","authors":"A. J. Badakaya, A. S. Halliru, J. Adamu","doi":"10.3934/JDG.2021019","DOIUrl":null,"url":null,"abstract":"We consider a pursuit-evasion differential game problem with countable number pursuers and one evader in the Hilbert space \\begin{document}$ l_{2}. $\\end{document} Players' dynamic equations described by certain \\begin{document}$ n^{th} $\\end{document} order ordinary differential equations. Control functions of the players subject to integral constraints. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. The stoppage time of the game is fixed and the game payoff is the distance between evader and closest pursuer when the game is stopped. We study this game problem and find the value of the game. In addition to this, we construct players' optimal strategies.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Game value for a pursuit-evasion differential game problem in a Hilbert space\",\"authors\":\"A. J. Badakaya, A. S. Halliru, J. Adamu\",\"doi\":\"10.3934/JDG.2021019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a pursuit-evasion differential game problem with countable number pursuers and one evader in the Hilbert space \\\\begin{document}$ l_{2}. $\\\\end{document} Players' dynamic equations described by certain \\\\begin{document}$ n^{th} $\\\\end{document} order ordinary differential equations. Control functions of the players subject to integral constraints. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. The stoppage time of the game is fixed and the game payoff is the distance between evader and closest pursuer when the game is stopped. We study this game problem and find the value of the game. In addition to this, we construct players' optimal strategies.\",\"PeriodicalId\":42722,\"journal\":{\"name\":\"Journal of Dynamics and Games\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamics and Games\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/JDG.2021019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Games","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/JDG.2021019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 3
摘要
We consider a pursuit-evasion differential game problem with countable number pursuers and one evader in the Hilbert space \begin{document}$ l_{2}. $\end{document} Players' dynamic equations described by certain \begin{document}$ n^{th} $\end{document} order ordinary differential equations. Control functions of the players subject to integral constraints. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. The stoppage time of the game is fixed and the game payoff is the distance between evader and closest pursuer when the game is stopped. We study this game problem and find the value of the game. In addition to this, we construct players' optimal strategies.
Game value for a pursuit-evasion differential game problem in a Hilbert space
We consider a pursuit-evasion differential game problem with countable number pursuers and one evader in the Hilbert space \begin{document}$ l_{2}. $\end{document} Players' dynamic equations described by certain \begin{document}$ n^{th} $\end{document} order ordinary differential equations. Control functions of the players subject to integral constraints. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. The stoppage time of the game is fixed and the game payoff is the distance between evader and closest pursuer when the game is stopped. We study this game problem and find the value of the game. In addition to this, we construct players' optimal strategies.
期刊介绍:
The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.