{"title":"退化g期望下随机最优控制问题的动态规划原理","authors":"Xiaojuan Li","doi":"10.1016/j.sysconle.2024.105988","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study a stochastic optimal control problem under degenerate <span><math><mi>G</mi></math></span>-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we obtain the dynamic programming principle, and prove that the value function is the unique viscosity solution to the related HJB equation under degenerate case.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 105988"},"PeriodicalIF":2.5000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamic programming principle for stochastic optimal control problem under degenerate G-expectation\",\"authors\":\"Xiaojuan Li\",\"doi\":\"10.1016/j.sysconle.2024.105988\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we study a stochastic optimal control problem under degenerate <span><math><mi>G</mi></math></span>-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we obtain the dynamic programming principle, and prove that the value function is the unique viscosity solution to the related HJB equation under degenerate case.</div></div>\",\"PeriodicalId\":49450,\"journal\":{\"name\":\"Systems & Control Letters\",\"volume\":\"196 \",\"pages\":\"Article 105988\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2025-02-01\",\"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/S0167691124002767\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/12/10 0:00:00\",\"PubModel\":\"Epub\",\"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/S0167691124002767","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/12/10 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Dynamic programming principle for stochastic optimal control problem under degenerate G-expectation
In this paper, we study a stochastic optimal control problem under degenerate -expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we obtain the dynamic programming principle, and prove that the value function is the unique viscosity solution to the related HJB equation under degenerate case.
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.
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