N. Papageorgiou, Vicentiu D. Rădulescu, Dušan D. Repovš
{"title":"最优控制问题的松弛方法","authors":"N. Papageorgiou, Vicentiu D. Rădulescu, Dušan D. Repovš","doi":"10.1142/S1664360720500046","DOIUrl":null,"url":null,"abstract":"We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map [Formula: see text]. We do not assume that [Formula: see text], incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The first one is an outgrowth of the reduction method from the existence theory, while the second method uses Young measures. We show that the two relaxation methods are equivalent and admissible.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"6 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2020-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Relaxation methods for optimal control problems\",\"authors\":\"N. Papageorgiou, Vicentiu D. Rădulescu, Dušan D. Repovš\",\"doi\":\"10.1142/S1664360720500046\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map [Formula: see text]. We do not assume that [Formula: see text], incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The first one is an outgrowth of the reduction method from the existence theory, while the second method uses Young measures. We show that the two relaxation methods are equivalent and admissible.\",\"PeriodicalId\":9348,\"journal\":{\"name\":\"Bulletin of Mathematical Sciences\",\"volume\":\"6 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2020-02-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of Mathematical Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/S1664360720500046\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/S1664360720500046","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map [Formula: see text]. We do not assume that [Formula: see text], incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The first one is an outgrowth of the reduction method from the existence theory, while the second method uses Young measures. We show that the two relaxation methods are equivalent and admissible.
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The Bulletin of Mathematical Sciences, a peer-reviewed, open access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (up to 15 pages) containing significant results of wider interest. Most of the expository articles will be invited.
The Bulletin of Mathematical Sciences is launched by King Abdulaziz University, Jeddah, Saudi Arabia.
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