流量边界条件扰动下不稳定热方程的快速稳定化

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2025-02-01 DOI:10.1016/j.sysconle.2024.105973

Patricio Guzmán, Esteban Hernández

{"title":"流量边界条件扰动下不稳定热方程的快速稳定化","authors":"Patricio Guzmán, Esteban Hernández","doi":"10.1016/j.sysconle.2024.105973","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper we prove the rapid stabilization of an unstable heat equation subjected to an unknown disturbance, which is assumed to be acting at the flux boundary condition. To that end, we design a multivalued feedback law by employing the backstepping method, Lyapunov techniques and the sign multivalued operator, which is used to handle the effects of the unknown disturbance. The well-posedness of the closed-loop system, which is a differential inclusion, is shown with the maximal monotone operator theory.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 105973"},"PeriodicalIF":2.1000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rapid stabilization of an unstable heat equation with disturbance at the flux boundary condition\",\"authors\":\"Patricio Guzmán, Esteban Hernández\",\"doi\":\"10.1016/j.sysconle.2024.105973\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper we prove the rapid stabilization of an unstable heat equation subjected to an unknown disturbance, which is assumed to be acting at the flux boundary condition. To that end, we design a multivalued feedback law by employing the backstepping method, Lyapunov techniques and the sign multivalued operator, which is used to handle the effects of the unknown disturbance. The well-posedness of the closed-loop system, which is a differential inclusion, is shown with the maximal monotone operator theory.</div></div>\",\"PeriodicalId\":49450,\"journal\":{\"name\":\"Systems & Control Letters\",\"volume\":\"196 \",\"pages\":\"Article 105973\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2025-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems & Control Letters\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167691124002615\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691124002615","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 0

摘要

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

Rapid stabilization of an unstable heat equation with disturbance at the flux boundary condition

In this paper we prove the rapid stabilization of an unstable heat equation subjected to an unknown disturbance, which is assumed to be acting at the flux boundary condition. To that end, we design a multivalued feedback law by employing the backstepping method, Lyapunov techniques and the sign multivalued operator, which is used to handle the effects of the unknown disturbance. The well-posedness of the closed-loop system, which is a differential inclusion, is shown with the maximal monotone operator theory.

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

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.