{"title":"有界观测下反应扩散方程的调节","authors":"H. Lhachemi, C. Prieur","doi":"10.1137/1.9781611976847.11","DOIUrl":null,"url":null,"abstract":"This paper solves a regulation problem for a reaction-diffusion equation. More precisely, for a given bounded observation, we design a boundary controller so that the setpoint output of the equation converges to a prescribed reference signal. The control law is finite-dimensional and is obtained by coupling a pole-placement control law with an observer. The proofs are based on a Lyapunov function and relies on the properties of Sturm-Liouville operators.","PeriodicalId":356259,"journal":{"name":"2021 Proceedings of the Conference on Control and its Applications","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regulation of a reaction-diffusion equation with bounded observation\",\"authors\":\"H. Lhachemi, C. Prieur\",\"doi\":\"10.1137/1.9781611976847.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper solves a regulation problem for a reaction-diffusion equation. More precisely, for a given bounded observation, we design a boundary controller so that the setpoint output of the equation converges to a prescribed reference signal. The control law is finite-dimensional and is obtained by coupling a pole-placement control law with an observer. The proofs are based on a Lyapunov function and relies on the properties of Sturm-Liouville operators.\",\"PeriodicalId\":356259,\"journal\":{\"name\":\"2021 Proceedings of the Conference on Control and its Applications\",\"volume\":\"16 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 Proceedings of the Conference on Control and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/1.9781611976847.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 Proceedings of the Conference on Control and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/1.9781611976847.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Regulation of a reaction-diffusion equation with bounded observation
This paper solves a regulation problem for a reaction-diffusion equation. More precisely, for a given bounded observation, we design a boundary controller so that the setpoint output of the equation converges to a prescribed reference signal. The control law is finite-dimensional and is obtained by coupling a pole-placement control law with an observer. The proofs are based on a Lyapunov function and relies on the properties of Sturm-Liouville operators.
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