具有动态边界条件的一维热方程的对数凸性和脉冲可控性

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS IMA Journal of Mathematical Control and Information Pub Date : 2022-03-20 DOI:10.1093/imamci/dnac013

Salah-Eddine Chorfi, G. E. Guermai, L. Maniar, W. Zouhair

{"title":"具有动态边界条件的一维热方程的对数凸性和脉冲可控性","authors":"Salah-Eddine Chorfi, G. E. Guermai, L. Maniar, W. Zouhair","doi":"10.1093/imamci/dnac013","DOIUrl":null,"url":null,"abstract":"In this paper, we prove a logarithmic convexity that reflects an observability estimate at a single point of time for 1-D heat equation with dynamic boundary conditions. Consequently, we establish the impulse approximate controllability for the impulsive heat equation with dynamic boundary conditions. Moreover, we obtain an explicit upper bound of the cost of impulse control. At the end, we give a constructive algorithm for computing the impulsive control of minimal $L^2$-norm. We also present some numerical tests to validate the theoretical results and show the efficiency of the designed algorithm.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"2 1","pages":"861-891"},"PeriodicalIF":1.6000,"publicationDate":"2022-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Logarithmic convexity and impulsive controllability for the one-dimensional heat equation with dynamic boundary conditions\",\"authors\":\"Salah-Eddine Chorfi, G. E. Guermai, L. Maniar, W. Zouhair\",\"doi\":\"10.1093/imamci/dnac013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove a logarithmic convexity that reflects an observability estimate at a single point of time for 1-D heat equation with dynamic boundary conditions. Consequently, we establish the impulse approximate controllability for the impulsive heat equation with dynamic boundary conditions. Moreover, we obtain an explicit upper bound of the cost of impulse control. At the end, we give a constructive algorithm for computing the impulsive control of minimal $L^2$-norm. We also present some numerical tests to validate the theoretical results and show the efficiency of the designed algorithm.\",\"PeriodicalId\":56128,\"journal\":{\"name\":\"IMA Journal of Mathematical Control and Information\",\"volume\":\"2 1\",\"pages\":\"861-891\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2022-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IMA Journal of Mathematical Control and Information\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1093/imamci/dnac013\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Mathematical Control and Information","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1093/imamci/dnac013","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 6

摘要

本文证明了具有动态边界条件的一维热方程在单时间点上的可观测性估计的对数凸性。因此，我们建立了具有动态边界条件的脉冲热方程的脉冲近似可控性。此外，我们还得到了脉冲控制代价的一个显式上界。最后给出了最小L^2 -范数脉冲控制的构造算法。通过数值实验验证了理论结果，并证明了所设计算法的有效性。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Logarithmic convexity and impulsive controllability for the one-dimensional heat equation with dynamic boundary conditions

In this paper, we prove a logarithmic convexity that reflects an observability estimate at a single point of time for 1-D heat equation with dynamic boundary conditions. Consequently, we establish the impulse approximate controllability for the impulsive heat equation with dynamic boundary conditions. Moreover, we obtain an explicit upper bound of the cost of impulse control. At the end, we give a constructive algorithm for computing the impulsive control of minimal $L^2$-norm. We also present some numerical tests to validate the theoretical results and show the efficiency of the designed algorithm.

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

IMA Journal of Mathematical Control and Information 工程技术-应用数学

CiteScore

3.30

自引率

6.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal is to provide an outlet for papers which are original and of high quality in mathematical control theory, systems theory, and applied information sciences. Short papers and mathematical correspondence or technical notes will be welcome, although the primary function of the journal is to publish papers of substantial length and coverage. The emphasis will be upon relevance, originality and clarify of presentation, although timeliness may well be an important feature in acceptable papers. Speculative papers that suggest new avenues for research or potential solutions to unsolved problems of control and information theory will be particularly welcome. Specific application papers will not normally be within the remit of the journal. Applications that illustrate techniques or theories will be acceptable. A prime function of the journal is to encourage the interplay between control and information theory and other mathematical sciences. All submitted papers will be judged on their merits by at least two referees and a full paper report will be available to the intending authors. Submitted articles will in general be published in an issue within six months of submission. Papers should not have previously published, nor should they be undes consideration for publication in another journal. This Journal takes publication ethics very seriously. If misconduct is found or suspected after the manuscript is published, the journal will investigate the matter and this may result in the article subsequently being retracted.