{"title":"二维环面上线性分散 PDE 的精确可控性和稳定性","authors":"Francisco J. Vielma-Leal, Ademir Pastor","doi":"10.1137/22m1529361","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 539-562, February 2024. <br/> Abstract. The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE’s posed on the two-dimensional torus [math]. The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin–Ono and Korteweg–de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in the Sobolev space [math], with [math], by constructing an appropriated feedback control law.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exact Controllability and Stabilization for Linear Dispersive PDE’s on the Two-Dimensional Torus\",\"authors\":\"Francisco J. Vielma-Leal, Ademir Pastor\",\"doi\":\"10.1137/22m1529361\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 539-562, February 2024. <br/> Abstract. The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE’s posed on the two-dimensional torus [math]. The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin–Ono and Korteweg–de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in the Sobolev space [math], with [math], by constructing an appropriated feedback control law.\",\"PeriodicalId\":49531,\"journal\":{\"name\":\"SIAM Journal on Control and Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Control and Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1529361\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Control and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1529361","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Exact Controllability and Stabilization for Linear Dispersive PDE’s on the Two-Dimensional Torus
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 539-562, February 2024. Abstract. The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE’s posed on the two-dimensional torus [math]. The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin–Ono and Korteweg–de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in the Sobolev space [math], with [math], by constructing an appropriated feedback control law.
期刊介绍：
SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition.
The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.
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