{"title":"Feedback semiglobal stabilization to trajectories for the Kuramoto–Sivashinsky equation","authors":"Sérgio S Rodrigues;Dagmawi A Seifu","doi":"10.1093/imamci/dnac033","DOIUrl":null,"url":null,"abstract":"It is shown that an oblique projection-based feedback control is able to stabilize the state of the Kuramoto–Sivashinsky equation, evolving in rectangular domains, to a given time-dependent trajectory. The actuators consist of a finite number of indicator functions supported in small subdomains. Simulations are presented, in the one-dimensional case under periodic boundary conditions and in the two-dimensional case under Neumann boundary conditions, showing the stabilizing performance of the feedback control.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"40 1","pages":"38-80"},"PeriodicalIF":1.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Mathematical Control and Information","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10078816/","RegionNum":4,"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: 1
Abstract
It is shown that an oblique projection-based feedback control is able to stabilize the state of the Kuramoto–Sivashinsky equation, evolving in rectangular domains, to a given time-dependent trajectory. The actuators consist of a finite number of indicator functions supported in small subdomains. Simulations are presented, in the one-dimensional case under periodic boundary conditions and in the two-dimensional case under Neumann boundary conditions, showing the stabilizing performance of the feedback control.
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