{"title":"Stochastic maximum principle for optimal control problems with mixed delays and noisy observations","authors":"Heping Ma , Yu Shi","doi":"10.1016/j.ejcon.2024.101073","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study the optimal control problem for the state governed by stochastic differential equation with delay and partially observed by a noisy process. Some variational inequalities and a necessary condition for optimality are established. Meanwhile, we introduce two kinds of adjoint equation which are shown to be equivalent. As an application, a linear–quadratic system and a financial problem are presented to demonstrate our results. In particular, its numerical simulation and some figures are used to illustrate the effect of delay on optimal solutions.</p></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Control","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S094735802400133X","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the optimal control problem for the state governed by stochastic differential equation with delay and partially observed by a noisy process. Some variational inequalities and a necessary condition for optimality are established. Meanwhile, we introduce two kinds of adjoint equation which are shown to be equivalent. As an application, a linear–quadratic system and a financial problem are presented to demonstrate our results. In particular, its numerical simulation and some figures are used to illustrate the effect of delay on optimal solutions.
期刊介绍：
The European Control Association (EUCA) has among its objectives to promote the development of the discipline. Apart from the European Control Conferences, the European Journal of Control is the Association''s main channel for the dissemination of important contributions in the field.
The aim of the Journal is to publish high quality papers on the theory and practice of control and systems engineering.
The scope of the Journal will be wide and cover all aspects of the discipline including methodologies, techniques and applications.
Research in control and systems engineering is necessary to develop new concepts and tools which enhance our understanding and improve our ability to design and implement high performance control systems. Submitted papers should stress the practical motivations and relevance of their results.
The design and implementation of a successful control system requires the use of a range of techniques:
Modelling
Robustness Analysis
Identification
Optimization
Control Law Design
Numerical analysis
Fault Detection, and so on.
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