{"title":"An Explicit Solution to a Discrete-time Stochastic Optimal Control Problem","authors":"M. Lefebvre","doi":"10.37394/23202.2023.22.40","DOIUrl":null,"url":null,"abstract":"The problem of controlling a one-dimensional Markov chain until is leaves a given set C is considered. The optimizer tries to minimize the time spent by the Markov chain inside C. The control variable can take two different values. An exact formula is obtained for the value function, from which the optimal control is deduced.","PeriodicalId":39422,"journal":{"name":"WSEAS Transactions on Systems and Control","volume":"256 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Systems and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23202.2023.22.40","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
The problem of controlling a one-dimensional Markov chain until is leaves a given set C is considered. The optimizer tries to minimize the time spent by the Markov chain inside C. The control variable can take two different values. An exact formula is obtained for the value function, from which the optimal control is deduced.
期刊介绍：
WSEAS Transactions on Systems and Control publishes original research papers relating to systems theory and automatic control. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with systems theory, dynamical systems, linear and non-linear control, intelligent control, robotics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.
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