整数阶积分-微分方程的零可控性

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

IMA Journal of Mathematical Control and Information Pub Date : 2023-05-04 DOI:10.1093/imamci/dnad013

Xiuxiang Zhou, Li Cheng, Xin Wang

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引用次数: 0

摘要

本文研究了整阶积分微分方程的零可控性问题。与偏微分方程的已知结果不同，我们需要考虑涉及拉普拉斯算子$(-\varDelta)^\beta $幂和一个积分项的方程。关键是在最终时刻构造一个合适的被控系统状态空间。首先讨论了一类双曲型积分微分方程。利用ingham型估计证明了被控系统是零可控的。并给出了控制时间。另一方面，通过谬论化简，我们推导出了一类具有$\beta \in \mathbb{N}^+$的抛物型积分微分方程的零可控性不成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the null controllability of integer order integro-differential equations

This paper is addressed to the study of the null controllability for integer order integro-differential equations. Unlike the known results for partial differential equations, we need to consider the equation involving a $\beta -$power of the Laplace operator $(-\varDelta )^\beta $ and an integral term. The key point is to construct a suitable state space of the controlled system at the final time. We first discuss a class of hyperbolic integro-differential equation. We prove that the controlled system is null controllable by an Ingham-type estimate. Also, the controllability time is given. On the other hand, by reduction to absurdity, we deduce that the null controllability property fails for a class of parabolic integro-differential equation with $\beta \in \mathbb{N}^+$.

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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.