Flatness Approach for the Boundary Controllability of a System of Heat Equations

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-06-19 DOI:10.1137/23m1577833

Blaise Colle, Jérôme Lohéac, Takéo Takahashi

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1766-1782, June 2024.
Abstract. We study the boundary controllability of [math] system of heat equations by using a flatness approach. According to the relation between the diffusion coefficients of the heat equation, it is known that the system can be neither null-controllable nor null-controllable for any [math], where [math]. Here we recover this result in the case that [math] by using the flatness method, and we obtain an explicit formula for the control and for the corresponding solutions. In particular, the state and the control have Gevrey regularity in time and in space.

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热方程组边界可控性的平整度方法

SIAM 控制与优化期刊》第 62 卷第 3 期第 1766-1782 页，2024 年 6 月。摘要。我们用平整度方法研究了[math]热方程组的边界可控性。根据热方程扩散系数之间的关系可知，对于任意[math]，其中[math]，系统既不可能是空可控的，也不可能是空可控的。在这里，我们通过平差法在 [math] 的情况下恢复了这一结果，并得到了控制和相应解的显式。特别是，状态和控制在时间和空间上都具有 Gevrey 正则性。

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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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

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.