{"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}
引用次数: 0
Abstract
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.
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.
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