{"title":"论控制问题中的均衡,并应用于演化系统","authors":"Radu Precup, Andrei Stan","doi":"arxiv-2409.09805","DOIUrl":null,"url":null,"abstract":"In this paper we examine a mutual control problem for systems of two abstract\nevolution equations subject to a proportionality final condition. Related\nobservability and semi-observability problems are discussed. The analysis\nemploys a vector fixed-point approach, using matrices rather than constants,\nand applies the technique of Bielecki equivalent norms.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On equilibrium in control problems with applications to evolution systems\",\"authors\":\"Radu Precup, Andrei Stan\",\"doi\":\"arxiv-2409.09805\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we examine a mutual control problem for systems of two abstract\\nevolution equations subject to a proportionality final condition. Related\\nobservability and semi-observability problems are discussed. The analysis\\nemploys a vector fixed-point approach, using matrices rather than constants,\\nand applies the technique of Bielecki equivalent norms.\",\"PeriodicalId\":501165,\"journal\":{\"name\":\"arXiv - MATH - Analysis of PDEs\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Analysis of PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09805\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09805","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On equilibrium in control problems with applications to evolution systems
In this paper we examine a mutual control problem for systems of two abstract
evolution equations subject to a proportionality final condition. Related
observability and semi-observability problems are discussed. The analysis
employs a vector fixed-point approach, using matrices rather than constants,
and applies the technique of Bielecki equivalent norms.