抛物型耦合系统的反馈镇定及其数值研究

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/mcrf.2023022

Wasim Akram, Debanjana Mitra, Neela Nataraj, Mythily Ramaswamy

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引用次数: 0

摘要

在本文的第一部分，我们研究了利用局部内部控制的抛物型耦合系统的反馈镇定问题。对于任意$ \omega>0 $，系统具有指数衰减$ -\omega<0 $的反馈稳定性。通过求解一个合适的代数Riccati方程，找到了反馈形式的稳定控制。在第二部分中，用有限维离散系统逼近连续系统时，采用了一致的有限元方法。对于任意$ \epsilon>0 $，该近似系统具有指数衰减$ -\omega+\epsilon $的反馈稳定性，并通过求解离散代数Riccati方程得到反馈控制。得到了稳定解的误差估计和稳定反馈控制。通过数值实现验证了理论结果。

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Feedback stabilization of a parabolic coupled system and its numerical study

In the first part of this article, we study feedback stabilization of a parabolic coupled system by using localized interior controls. The system is feedback stabilizable with exponential decay $ -\omega<0 $ for any $ \omega>0 $. A stabilizing control is found in feedback form by solving a suitable algebraic Riccati equation. In the second part, a conforming finite element method is employed to approximate the continuous system by a finite dimensional discrete system. The approximated system is also feedback stabilizable (uniformly) with exponential decay $ -\omega+\epsilon $, for any $ \epsilon>0 $ and the feedback control is obtained by solving a discrete algebraic Riccati equation. The error estimate of stabilized solutions as well as stabilizing feedback controls are obtained. We validate the theoretical results by numerical implementations.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.