{"title":"KdV 系统的快速和有限时间边界稳定","authors":"Hoai-Minh Nguyen","doi":"arxiv-2409.11768","DOIUrl":null,"url":null,"abstract":"We construct a static feedback control in a trajectory sense and a dynamic\nfeedback control to obtain the local rapid boundary stabilization of a KdV\nsystem using Gramian operators. We also construct a time-varying feedback\ncontrol in the trajectory sense and a time varying dynamic feedback control to\nreach the local finite-time boundary stabilization for the same system.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rapid and finite-time boundary stabilization of a KdV system\",\"authors\":\"Hoai-Minh Nguyen\",\"doi\":\"arxiv-2409.11768\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct a static feedback control in a trajectory sense and a dynamic\\nfeedback control to obtain the local rapid boundary stabilization of a KdV\\nsystem using Gramian operators. We also construct a time-varying feedback\\ncontrol in the trajectory sense and a time varying dynamic feedback control to\\nreach the local finite-time boundary stabilization for the same system.\",\"PeriodicalId\":501286,\"journal\":{\"name\":\"arXiv - MATH - Optimization and Control\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Optimization and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11768\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Optimization and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11768","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Rapid and finite-time boundary stabilization of a KdV system
We construct a static feedback control in a trajectory sense and a dynamic
feedback control to obtain the local rapid boundary stabilization of a KdV
system using Gramian operators. We also construct a time-varying feedback
control in the trajectory sense and a time varying dynamic feedback control to
reach the local finite-time boundary stabilization for the same system.
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