{"title":"Kuramoto–Sivashinsky方程轨迹的反馈半全局稳定","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":"{\"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}","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}
Feedback semiglobal stabilization to trajectories for the Kuramoto–Sivashinsky equation
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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