子扩散的随机最大原则及其应用

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-03-14 DOI:10.1137/23m157168x

Shuaiqi Zhang, Zhen-Qing Chen

{"title":"子扩散的随机最大原则及其应用","authors":"Shuaiqi Zhang, Zhen-Qing Chen","doi":"10.1137/23m157168x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 953-981, April 2024. <br/> Abstract. In this paper, we study optimal stochastic control problems for stochastic systems driven by non-Markov subdiffusion [math], which have mixed features of deterministic and stochastic controls. Here [math] is the standard Brownian motion on [math], and [math] is the inverse of a subordinator [math] with drift [math] that is independent of [math]. We obtain stochastic maximum principles (SMPs) for these systems using both convex and spiking variational methods, depending on whether or not the domain is convex. To derive SMPs, we first establish a martingale representation theorem for subdiffusions [math], and then use it to derive the existence and uniqueness result for the solutions of backward stochastic differential equations (BSDEs) driven by subdiffusions, which may be of independent interest. We also derive sufficient SMPs. Application to a linear quadratic system is given to illustrate the main results of this paper.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stochastic Maximum Principle for Subdiffusions and Its Applications\",\"authors\":\"Shuaiqi Zhang, Zhen-Qing Chen\",\"doi\":\"10.1137/23m157168x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 953-981, April 2024. <br/> Abstract. In this paper, we study optimal stochastic control problems for stochastic systems driven by non-Markov subdiffusion [math], which have mixed features of deterministic and stochastic controls. Here [math] is the standard Brownian motion on [math], and [math] is the inverse of a subordinator [math] with drift [math] that is independent of [math]. We obtain stochastic maximum principles (SMPs) for these systems using both convex and spiking variational methods, depending on whether or not the domain is convex. To derive SMPs, we first establish a martingale representation theorem for subdiffusions [math], and then use it to derive the existence and uniqueness result for the solutions of backward stochastic differential equations (BSDEs) driven by subdiffusions, which may be of independent interest. We also derive sufficient SMPs. Application to a linear quadratic system is given to illustrate the main results of this paper.\",\"PeriodicalId\":49531,\"journal\":{\"name\":\"SIAM Journal on Control and Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-03-14\",\"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/10.1137/23m157168x\",\"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/10.1137/23m157168x","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 2 期第 953-981 页，2024 年 4 月。摘要本文研究由非马尔可夫子扩散[math]驱动的随机系统的最优随机控制问题，该问题具有确定性控制和随机控制的混合特征。这里的[math]是[math]上的标准布朗运动，[math]是与[math]无关的漂移[math]的从动[math]的逆。我们使用凸变分法和尖峰变分法（取决于域是否凸）来获得这些系统的随机最大原则（SMPs）。为了推导 SMPs，我们首先建立了子扩散的马丁格尔表示定理[math]，然后利用它推导出由子扩散驱动的后向随机微分方程（BSDEs）解的存在性和唯一性结果，这可能是我们感兴趣的独立问题。我们还推导出了充分的 SMP。本文还给出了线性二次系统的应用，以说明本文的主要结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Stochastic Maximum Principle for Subdiffusions and Its Applications

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 953-981, April 2024.
Abstract. In this paper, we study optimal stochastic control problems for stochastic systems driven by non-Markov subdiffusion [math], which have mixed features of deterministic and stochastic controls. Here [math] is the standard Brownian motion on [math], and [math] is the inverse of a subordinator [math] with drift [math] that is independent of [math]. We obtain stochastic maximum principles (SMPs) for these systems using both convex and spiking variational methods, depending on whether or not the domain is convex. To derive SMPs, we first establish a martingale representation theorem for subdiffusions [math], and then use it to derive the existence and uniqueness result for the solutions of backward stochastic differential equations (BSDEs) driven by subdiffusions, which may be of independent interest. We also derive sufficient SMPs. Application to a linear quadratic system is given to illustrate the main results of this paper.

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.