{"title":"Robust output regulation for multi-dimensional heat equation under boundary control","authors":"Ren-Xi Zhao , Bao-Zhu Guo , Lassi Paunonen","doi":"10.1016/j.automatica.2024.111956","DOIUrl":null,"url":null,"abstract":"<div><div>Over the past few years, the internal model principle has been extended to some systems described by one-dimensional partial differential equations (PDEs) from the PDE perspective. However, robustness has remained limited to specific cases, primarily due to the challenges in formulating it within the PDE framework. In this paper, we explore output regulation for a multi-dimensional heat equation under boundary control, where the output space is infinite-dimensional. We not only derive an analytic tracking error feedback control but also demonstrate robustness. This is achieved by leveraging abstract results and PDE design techniques.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824004503","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
Over the past few years, the internal model principle has been extended to some systems described by one-dimensional partial differential equations (PDEs) from the PDE perspective. However, robustness has remained limited to specific cases, primarily due to the challenges in formulating it within the PDE framework. In this paper, we explore output regulation for a multi-dimensional heat equation under boundary control, where the output space is infinite-dimensional. We not only derive an analytic tracking error feedback control but also demonstrate robustness. This is achieved by leveraging abstract results and PDE design techniques.
期刊介绍：
Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field.
After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience.
Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.
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