{"title":"Sampled-data finite-dimensional boundary control for 1-D Burgers’ equation","authors":"Lina Pan , Pengfei Wang , Emilia Fridman","doi":"10.1016/j.ifacol.2024.10.149","DOIUrl":null,"url":null,"abstract":"<div><div><span>In this paper, we are concerned with the regional exponential stabilization of a 1-D Burgers’ equation under Neumann actuation via modal decomposition method and dynamic extension. We consider a sampled-data finite-dimensional boundary control, which is implemented via a generalized hold device. We use Wirtinger-based piecewise continuous-time Lyapunov functional to compensate sampling of the finite-dimensional state, and provide the</span> <em>H</em><sup>1</sup><span>-stability analysis for the full-order closed-loop system. Given a decay rate, we provide the efficient linear matrix inequality (LMI) conditions for finding the controller dimension and gain, as well as a bound on the domain of attraction. We prove that for some fixed upper bounds on the initial value and sampling intervals, the feasibility of LMIs for some N (dimension of the controller) implies their feasibility for N + 1. Numerical example illustrates the efficiency of the proposed method.</span></div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"58 17","pages":"Pages 172-177"},"PeriodicalIF":0.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IFAC-PapersOnLine","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2405896324019049","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
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Abstract
In this paper, we are concerned with the regional exponential stabilization of a 1-D Burgers’ equation under Neumann actuation via modal decomposition method and dynamic extension. We consider a sampled-data finite-dimensional boundary control, which is implemented via a generalized hold device. We use Wirtinger-based piecewise continuous-time Lyapunov functional to compensate sampling of the finite-dimensional state, and provide theH1-stability analysis for the full-order closed-loop system. Given a decay rate, we provide the efficient linear matrix inequality (LMI) conditions for finding the controller dimension and gain, as well as a bound on the domain of attraction. We prove that for some fixed upper bounds on the initial value and sampling intervals, the feasibility of LMIs for some N (dimension of the controller) implies their feasibility for N + 1. Numerical example illustrates the efficiency of the proposed method.
期刊介绍：
All papers from IFAC meetings are published, in partnership with Elsevier, the IFAC Publisher, in theIFAC-PapersOnLine proceedings series hosted at the ScienceDirect web service. This series includes papers previously published in the IFAC website.The main features of the IFAC-PapersOnLine series are: -Online archive including papers from IFAC Symposia, Congresses, Conferences, and most Workshops. -All papers accepted at the meeting are published in PDF format - searchable and citable. -All papers published on the web site can be cited using the IFAC PapersOnLine ISSN and the individual paper DOI (Digital Object Identifier). The site is Open Access in nature - no charge is made to individuals for reading or downloading. Copyright of all papers belongs to IFAC and must be referenced if derivative journal papers are produced from the conference papers. All papers published in IFAC-PapersOnLine have undergone a peer review selection process according to the IFAC rules.
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