G. I. Ibragimov, X. Sh. Qo’shaqov, A. A. Muxammadjonov
{"title":"Optimal Pursuit Differential Game Problem for an Infinite System of Binary Differential Equations","authors":"G. I. Ibragimov, X. Sh. Qo’shaqov, A. A. Muxammadjonov","doi":"10.1134/s1995080224600821","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We study a differential game problem for an infinite system of binary differential equations. The control functions of pursuer and evader are subjected to integral constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space <span>\\(l_{2}\\)</span> and the aim of the evader is opposite. An equation for the optimal pursuit time is obtained and optimal controls of players are constructed. Also, an auxiliary optimal control problem is solved to prove the main result of the paper.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"71 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224600821","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study a differential game problem for an infinite system of binary differential equations. The control functions of pursuer and evader are subjected to integral constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space \(l_{2}\) and the aim of the evader is opposite. An equation for the optimal pursuit time is obtained and optimal controls of players are constructed. Also, an auxiliary optimal control problem is solved to prove the main result of the paper.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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