{"title":"Hierarchical control problem for the heat equation with dynamic boundary conditions","authors":"Omar Oukdach, Idriss Boutaayamou, Lahcen Maniar","doi":"10.1093/imamci/dnae009","DOIUrl":null,"url":null,"abstract":"This paper deals with a hierarchical control problem for the heat equation with dynamic boundary conditions. The main goal consists of letting the state near from a prescribed target in a fixed observation region. The secondary objective is the null controllability. In other words, we reverse the roles of the leader and the follower addressed in the recent article. For this purpose, we combine some appropriate Carleman estimates and the Stackelberg strategy. We also extend our study for hierarchical-biobjective problems by applying the Stackelberg–Pareto strategy.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Mathematical Control and Information","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1093/imamci/dnae009","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper deals with a hierarchical control problem for the heat equation with dynamic boundary conditions. The main goal consists of letting the state near from a prescribed target in a fixed observation region. The secondary objective is the null controllability. In other words, we reverse the roles of the leader and the follower addressed in the recent article. For this purpose, we combine some appropriate Carleman estimates and the Stackelberg strategy. We also extend our study for hierarchical-biobjective problems by applying the Stackelberg–Pareto strategy.
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