{"title":"The minimal hitting probability of continuous-time controlled Markov systems with countable states","authors":"Yanyun Li , Junping Li","doi":"10.1016/j.sysconle.2024.106002","DOIUrl":null,"url":null,"abstract":"<div><div>This paper concentrates on the minimal hitting probability of continuous-time controlled Markov systems (CTCMSs) with countable state and finite admissible action spaces. The existence of an optimal policy is first proved. In particular, for a special and important case of controlled branching processes (CBPs), it is proved that the minimal hitting probability is the unique solution to an improved optimal system of equations. Furthermore, a novel and precise improved-policy iteration algorithm of an optimal policy and the minimal hitting probability (minimal extinction probability) is presented for CBPs.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 106002"},"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/S0167691124002901","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}
引用次数: 0
Abstract
This paper concentrates on the minimal hitting probability of continuous-time controlled Markov systems (CTCMSs) with countable state and finite admissible action spaces. The existence of an optimal policy is first proved. In particular, for a special and important case of controlled branching processes (CBPs), it is proved that the minimal hitting probability is the unique solution to an improved optimal system of equations. Furthermore, a novel and precise improved-policy iteration algorithm of an optimal policy and the minimal hitting probability (minimal extinction probability) is presented for CBPs.
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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