{"title":"Finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation","authors":"Yu-Shuo Shang , Ze-Hao Wu , Hua-Cheng Zhou","doi":"10.1016/j.sysconle.2025.106046","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we investigate the finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation with nonlinear multiplicative noise and non-local sensing measurement. We adopt the modal decomposition to divide the system into two subsystems: one unstable with finite positive eigenvalues and the other essentially stable. We design the controller for the unstable subsystem by dynamic extension and demonstrate that the proposed controller actually leads to the resulting closed-loop system to be well-posed and exponentially stable, both in the mean square and almost sure senses. Finally, some numerical simulations are performed to illustrate the effectiveness of the proposed method.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"197 ","pages":"Article 106046"},"PeriodicalIF":2.1000,"publicationDate":"2025-02-18","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/S0167691125000283","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 article, we investigate the finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation with nonlinear multiplicative noise and non-local sensing measurement. We adopt the modal decomposition to divide the system into two subsystems: one unstable with finite positive eigenvalues and the other essentially stable. We design the controller for the unstable subsystem by dynamic extension and demonstrate that the proposed controller actually leads to the resulting closed-loop system to be well-posed and exponentially stable, both in the mean square and almost sure senses. Finally, some numerical simulations are performed to illustrate the effectiveness of the proposed method.
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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