José E. Márquez-Prado , Onésimo Hernández-Lerma , Héctor Jasso-Fuentes
{"title":"Myopic optimal strategies for a class of continuous-time deterministic and stochastic control problems","authors":"José E. Márquez-Prado , Onésimo Hernández-Lerma , Héctor Jasso-Fuentes","doi":"10.1016/j.sysconle.2024.106016","DOIUrl":null,"url":null,"abstract":"<div><div>We give conditions for a class of continuous-time deterministic and stochastic optimal control problems to have <em>myopic optimal strategies</em>, that is, optimal controls obtained by solving optimization problems independent of the state trajectory. We show how these sufficient conditions are the same for the deterministic and stochastic cases, which means that the <em>certainty equivalence principle</em> is satisfied. Moreover, for the infinite-horizon time-homogeneous case, myopic optimal strategies are obtained by solving a single optimization problem; hence, optimal controls are constant functions.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 106016"},"PeriodicalIF":2.1000,"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/S0167691124003049","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}
Myopic optimal strategies for a class of continuous-time deterministic and stochastic control problems
We give conditions for a class of continuous-time deterministic and stochastic optimal control problems to have myopic optimal strategies, that is, optimal controls obtained by solving optimization problems independent of the state trajectory. We show how these sufficient conditions are the same for the deterministic and stochastic cases, which means that the certainty equivalence principle is satisfied. Moreover, for the infinite-horizon time-homogeneous case, myopic optimal strategies are obtained by solving a single optimization problem; hence, optimal controls are constant functions.
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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