分数布朗运动驱动的部分观测随机系统最优控制的全局最大原则

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-02-06 DOI:10.1137/22m1543203

Yueyang Zheng, Yaozhong Hu

{"title":"分数布朗运动驱动的部分观测随机系统最优控制的全局最大原则","authors":"Yueyang Zheng, Yaozhong Hu","doi":"10.1137/22m1543203","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 509-538, February 2024. <br/> Abstract. In this paper we study the stochastic control problem of a partially observed (multidimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov transformation, we introduce and study new stochastic processes which are used to transform the original problem to a “classical one”. The adjoint backward stochastic differential equations and the necessary condition satisfied by the optimal control (maximum principle) are obtained.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion\",\"authors\":\"Yueyang Zheng, Yaozhong Hu\",\"doi\":\"10.1137/22m1543203\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 509-538, February 2024. <br/> Abstract. In this paper we study the stochastic control problem of a partially observed (multidimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov transformation, we introduce and study new stochastic processes which are used to transform the original problem to a “classical one”. The adjoint backward stochastic differential equations and the necessary condition satisfied by the optimal control (maximum principle) are obtained.\",\"PeriodicalId\":49531,\"journal\":{\"name\":\"SIAM Journal on Control and Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-02-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Control and Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1543203\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Control and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1543203","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 1 期第 509-538 页，2024 年 2 月。摘要本文研究了由布朗运动和分数布朗运动驱动的部分观测（多维）随机系统的随机控制问题。在缺乏吉尔萨诺夫变换这一有力工具的情况下，我们引入并研究了新的随机过程，用来将原始问题转换为 "经典问题"。我们得到了邻接后向随机微分方程和最优控制所需的必要条件（最大原则）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 509-538, February 2024.
Abstract. In this paper we study the stochastic control problem of a partially observed (multidimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov transformation, we introduce and study new stochastic processes which are used to transform the original problem to a “classical one”. The adjoint backward stochastic differential equations and the necessary condition satisfied by the optimal control (maximum principle) are obtained.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.