{"title":"控制非线性水波:Korteweg-de Vries-Burgers方程的边界稳定","authors":"Weijiu Liu, M. Krstić","doi":"10.1109/ACC.1999.786108","DOIUrl":null,"url":null,"abstract":"The problem of global exponential stabilization by boundary feedback for the Korteweg-de Vries-Burgers equation on the domain [0,1] is considered. We derive a control law of the form u(0)=u/sub x/(1)=u/sub xx/(1)-k[u(1)/sup 3/+ u(1)]=0, where k is a sufficiently large positive constant, and prove that it guarantees L/sup 2/-global exponential stability, H/sup 1/-global asymptotic stability, and H/sup 1/ semi-global exponential stability. The closed-loop system is shown to be well posed.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Controlling nonlinear water waves: boundary stabilization of the Korteweg-de Vries-Burgers equation\",\"authors\":\"Weijiu Liu, M. Krstić\",\"doi\":\"10.1109/ACC.1999.786108\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of global exponential stabilization by boundary feedback for the Korteweg-de Vries-Burgers equation on the domain [0,1] is considered. We derive a control law of the form u(0)=u/sub x/(1)=u/sub xx/(1)-k[u(1)/sup 3/+ u(1)]=0, where k is a sufficiently large positive constant, and prove that it guarantees L/sup 2/-global exponential stability, H/sup 1/-global asymptotic stability, and H/sup 1/ semi-global exponential stability. The closed-loop system is shown to be well posed.\",\"PeriodicalId\":441363,\"journal\":{\"name\":\"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)\",\"volume\":\"27 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-06-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ACC.1999.786108\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACC.1999.786108","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Controlling nonlinear water waves: boundary stabilization of the Korteweg-de Vries-Burgers equation
The problem of global exponential stabilization by boundary feedback for the Korteweg-de Vries-Burgers equation on the domain [0,1] is considered. We derive a control law of the form u(0)=u/sub x/(1)=u/sub xx/(1)-k[u(1)/sup 3/+ u(1)]=0, where k is a sufficiently large positive constant, and prove that it guarantees L/sup 2/-global exponential stability, H/sup 1/-global asymptotic stability, and H/sup 1/ semi-global exponential stability. The closed-loop system is shown to be well posed.
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