{"title":"双曲平衡律多维系统的镇定","authors":"Michael Herty, Ferdinand Thein","doi":"10.3934/mcrf.2023033","DOIUrl":null,"url":null,"abstract":"We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $ \\mathbb{R}^n $. A reformulation leads to a stabilization problem for a multi-dimensional system of $ n $ hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $ L^2 $ for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Stabilization of a multi-dimensional system of hyperbolic balance laws\",\"authors\":\"Michael Herty, Ferdinand Thein\",\"doi\":\"10.3934/mcrf.2023033\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $ \\\\mathbb{R}^n $. A reformulation leads to a stabilization problem for a multi-dimensional system of $ n $ hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $ L^2 $ for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/mcrf.2023033\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/mcrf.2023033","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Stabilization of a multi-dimensional system of hyperbolic balance laws
We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $ \mathbb{R}^n $. A reformulation leads to a stabilization problem for a multi-dimensional system of $ n $ hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $ L^2 $ for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.