{"title":"Existence of Optimal Sets for Linear Variational Equations and Inequalities","authors":"V. G. Zamuraev","doi":"10.1134/s0012266124060053","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper considers an optimal control problem in which the plant is described by a linear\nfunctional equation in a Hilbert space and a control action is a change of the space. Sufficient\nconditions for the existence of a solution are obtained. The results are generalized to the case in\nwhich the plant is described by a linear variational inequality.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"100 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124060053","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper considers an optimal control problem in which the plant is described by a linear
functional equation in a Hilbert space and a control action is a change of the space. Sufficient
conditions for the existence of a solution are obtained. The results are generalized to the case in
which the plant is described by a linear variational inequality.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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