{"title":"具有时变延迟的控制系统的随机最大原则","authors":"Yuecai Han , Yuhang Li","doi":"10.1016/j.sysconle.2024.105864","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study the stochastic optimal control problem for control systems with time-varying delay. The corresponding state equation is a kind of stochastic differential delay equation. A kind of anticipated backward stochastic differential equations is introduced, and the existence and uniqueness of the solution are proved. Then we obtain the stochastic maximum principle for the control systems with time-varying delay. As an application, the linear quadratic control problem is investigated to illustrate the main results.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stochastic maximum principle for control systems with time-varying delay\",\"authors\":\"Yuecai Han , Yuhang Li\",\"doi\":\"10.1016/j.sysconle.2024.105864\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we study the stochastic optimal control problem for control systems with time-varying delay. The corresponding state equation is a kind of stochastic differential delay equation. A kind of anticipated backward stochastic differential equations is introduced, and the existence and uniqueness of the solution are proved. Then we obtain the stochastic maximum principle for the control systems with time-varying delay. As an application, the linear quadratic control problem is investigated to illustrate the main results.</p></div>\",\"PeriodicalId\":49450,\"journal\":{\"name\":\"Systems & Control Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-07-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems & Control Letters\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S016769112400152X\",\"RegionNum\":3,\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016769112400152X","RegionNum":3,"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}
Stochastic maximum principle for control systems with time-varying delay
In this paper, we study the stochastic optimal control problem for control systems with time-varying delay. The corresponding state equation is a kind of stochastic differential delay equation. A kind of anticipated backward stochastic differential equations is introduced, and the existence and uniqueness of the solution are proved. Then we obtain the stochastic maximum principle for the control systems with time-varying delay. As an application, the linear quadratic control problem is investigated to illustrate the main results.
期刊介绍:
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.