{"title":"边界控制下匹配谐波扰动波动方程的自适应镇定","authors":"Jun-Jun Liu, Yanxiao Zhao","doi":"10.1093/imamci/dnad010","DOIUrl":null,"url":null,"abstract":"\n In this paper, we are concerned with adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance. We use the adaptive and Lyapunov approach to estimate unknown disturbance and construct an adaptive boundary feedback controller. By the semigroup theory and Lasalle‘s invariance theorem, the well-posedness and asymptotic stability of the closed-loop system is proved, respectively. At the same time, it is shown that the parameter estimates involved in the constructed controller converge to their own real values as time goes to infinity. Some numerical simulations are offered at the end of the paper to illustrate the effectiveness of theoretical results.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"1 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2023-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance\",\"authors\":\"Jun-Jun Liu, Yanxiao Zhao\",\"doi\":\"10.1093/imamci/dnad010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n In this paper, we are concerned with adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance. We use the adaptive and Lyapunov approach to estimate unknown disturbance and construct an adaptive boundary feedback controller. By the semigroup theory and Lasalle‘s invariance theorem, the well-posedness and asymptotic stability of the closed-loop system is proved, respectively. At the same time, it is shown that the parameter estimates involved in the constructed controller converge to their own real values as time goes to infinity. Some numerical simulations are offered at the end of the paper to illustrate the effectiveness of theoretical results.\",\"PeriodicalId\":56128,\"journal\":{\"name\":\"IMA Journal of Mathematical Control and Information\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2023-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IMA Journal of Mathematical Control and Information\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1093/imamci/dnad010\",\"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://doi.org/10.1093/imamci/dnad010","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}
Adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance
In this paper, we are concerned with adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance. We use the adaptive and Lyapunov approach to estimate unknown disturbance and construct an adaptive boundary feedback controller. By the semigroup theory and Lasalle‘s invariance theorem, the well-posedness and asymptotic stability of the closed-loop system is proved, respectively. At the same time, it is shown that the parameter estimates involved in the constructed controller converge to their own real values as time goes to infinity. Some numerical simulations are offered at the end of the paper to illustrate the effectiveness of theoretical results.
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The Journal is to provide an outlet for papers which are original and of high quality in mathematical control theory, systems theory, and applied information sciences. Short papers and mathematical correspondence or technical notes will be welcome, although the primary function of the journal is to publish papers of substantial length and coverage. The emphasis will be upon relevance, originality and clarify of presentation, although timeliness may well be an important feature in acceptable papers. Speculative papers that suggest new avenues for research or potential solutions to unsolved problems of control and information theory will be particularly welcome. Specific application papers will not normally be within the remit of the journal. Applications that illustrate techniques or theories will be acceptable. A prime function of the journal is to encourage the interplay between control and information theory and other mathematical sciences.
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