{"title":"Optimal control for stochastic differential equations and related Kolmogorov equations","authors":"Ștefana-Lucia Aniţa","doi":"10.3934/eect.2022023","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>This paper concerns a stochastic optimal control problem with feedback Markov inputs. The problem is reduced to a deterministic optimal control problem for a Kolmogorov equation where the control for the deterministic problem is of open-loop type. The existence of an optimal control is proved for the deterministic control problem in a particular case. A maximum principle and some first order necessary optimality conditions are derived. Some examples and comments are discussed.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"25 5","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolution Equations and Control Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/eect.2022023","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
<p style='text-indent:20px;'>This paper concerns a stochastic optimal control problem with feedback Markov inputs. The problem is reduced to a deterministic optimal control problem for a Kolmogorov equation where the control for the deterministic problem is of open-loop type. The existence of an optimal control is proved for the deterministic control problem in a particular case. A maximum principle and some first order necessary optimality conditions are derived. Some examples and comments are discussed.</p>
期刊介绍:
EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include:
* Modeling of physical systems as infinite-dimensional processes
* Direct problems such as existence, regularity and well-posedness
* Stability, long-time behavior and associated dynamical attractors
* Indirect problems such as exact controllability, reachability theory and inverse problems
* Optimization - including shape optimization - optimal control, game theory and calculus of variations
* Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s)
* Applications of the theory to physics, chemistry, engineering, economics, medicine and biology