一维波动方程的非线性边界反馈控制

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) Pub Date : 2000-12-12 DOI:10.1109/CDC.2000.914097

Goong Chen, Tingwen Huang, S. Hsu

{"title":"一维波动方程的非线性边界反馈控制","authors":"Goong Chen, Tingwen Huang, S. Hsu","doi":"10.1109/CDC.2000.914097","DOIUrl":null,"url":null,"abstract":"In this paper, we analyze the dynamical behavior of the linear wave equation on an interval, where the right endpoint has a van der Pol type nonlinearity or boundary controller, while the left endpoint has a boundary condition involving displacement. The asymptotic behavior of the system can be classified into two basic types: classical unbounded instability, or spatial pointwise convergence to periodic points of a nonlinear map corresponding to the van der Pol condition.","PeriodicalId":217237,"journal":{"name":"Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)","volume":"28 6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2000-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Nonlinear boundary feedback control of the one-dimensional wave equation\",\"authors\":\"Goong Chen, Tingwen Huang, S. Hsu\",\"doi\":\"10.1109/CDC.2000.914097\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we analyze the dynamical behavior of the linear wave equation on an interval, where the right endpoint has a van der Pol type nonlinearity or boundary controller, while the left endpoint has a boundary condition involving displacement. The asymptotic behavior of the system can be classified into two basic types: classical unbounded instability, or spatial pointwise convergence to periodic points of a nonlinear map corresponding to the van der Pol condition.\",\"PeriodicalId\":217237,\"journal\":{\"name\":\"Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)\",\"volume\":\"28 6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2000-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.2000.914097\",\"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 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2000.914097","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

本文分析了线性波动方程在区间上的动力学行为，其中右端点具有van der Pol型非线性或边界控制器，而左端点具有涉及位移的边界条件。系统的渐近行为可分为两种基本类型:经典无界不稳定性，或对应于van der Pol条件的非线性映射的周期点的空间点向收敛。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Nonlinear boundary feedback control of the one-dimensional wave equation

In this paper, we analyze the dynamical behavior of the linear wave equation on an interval, where the right endpoint has a van der Pol type nonlinearity or boundary controller, while the left endpoint has a boundary condition involving displacement. The asymptotic behavior of the system can be classified into two basic types: classical unbounded instability, or spatial pointwise convergence to periodic points of a nonlinear map corresponding to the van der Pol condition.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)

自引率

0.00%

发文量