带有受限控制方向的零和停止器与奇异控制器博弈

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-07-19 DOI:10.1137/23m1579558

Andrea Bovo, Tiziano De Angelis, Jan Palczewski

{"title":"带有受限控制方向的零和停止器与奇异控制器博弈","authors":"Andrea Bovo, Tiziano De Angelis, Jan Palczewski","doi":"10.1137/23m1579558","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2203-2228, August 2024. <br/> Abstract. We consider a class of zero-sum stopper versus singular-controller games in which the controller can only act on a subset [math] of the [math] coordinates of a controlled diffusion. Due to the constraint on the control directions these games fall outside the framework of recently studied variational methods. In this paper we develop an approximation procedure, based on [math]-stability estimates for the controlled diffusion process and almost sure convergence of suitable stopping times. That allows us to prove existence of the game’s value and to obtain an optimal strategy for the stopper under continuity and growth conditions on the payoff functions. This class of games is a natural extension of (single-agent) singular control problems, studied in the literature, with similar constraints on the admissible controls.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Zero-Sum Stopper Versus Singular-Controller Games with Constrained Control Directions\",\"authors\":\"Andrea Bovo, Tiziano De Angelis, Jan Palczewski\",\"doi\":\"10.1137/23m1579558\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2203-2228, August 2024. <br/> Abstract. We consider a class of zero-sum stopper versus singular-controller games in which the controller can only act on a subset [math] of the [math] coordinates of a controlled diffusion. Due to the constraint on the control directions these games fall outside the framework of recently studied variational methods. In this paper we develop an approximation procedure, based on [math]-stability estimates for the controlled diffusion process and almost sure convergence of suitable stopping times. That allows us to prove existence of the game’s value and to obtain an optimal strategy for the stopper under continuity and growth conditions on the payoff functions. This class of games is a natural extension of (single-agent) singular control problems, studied in the literature, with similar constraints on the admissible controls.\",\"PeriodicalId\":49531,\"journal\":{\"name\":\"SIAM Journal on Control and Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-07-19\",\"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/10.1137/23m1579558\",\"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/10.1137/23m1579558","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 4 期，第 2203-2228 页，2024 年 8 月。摘要。我们考虑了一类零和阻塞与奇异控制器博弈，其中控制器只能作用于受控扩散的[数学]坐标子集[数学]。由于对控制方向的限制，这些博弈超出了最近研究的变分法框架。在本文中，我们基于受控扩散过程的[math]稳定性估计和合适的停止时间的几乎确定的收敛性，开发了一种近似程序。这样，我们就能证明博弈值的存在性，并在报酬函数的连续性和增长条件下为停止者获得最佳策略。这类博弈是（单个代理）奇异控制问题的自然延伸，在文献中已有研究，对可接受的控制也有类似的限制。

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

Zero-Sum Stopper Versus Singular-Controller Games with Constrained Control Directions

SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2203-2228, August 2024.
Abstract. We consider a class of zero-sum stopper versus singular-controller games in which the controller can only act on a subset [math] of the [math] coordinates of a controlled diffusion. Due to the constraint on the control directions these games fall outside the framework of recently studied variational methods. In this paper we develop an approximation procedure, based on [math]-stability estimates for the controlled diffusion process and almost sure convergence of suitable stopping times. That allows us to prove existence of the game’s value and to obtain an optimal strategy for the stopper under continuity and growth conditions on the payoff functions. This class of games is a natural extension of (single-agent) singular control problems, studied in the literature, with similar constraints on the admissible controls.

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.