Null Controllability of Coupled Parabolic Systems with Switching Control

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-11-16 DOI:10.1007/s00245-024-10197-4

Yuanhang Liu, Weijia Wu, Donghui Yang

引用次数: 0

Abstract

The focus of this paper is on the null controllability of two kinds of coupled systems including both degenerate and non-degenerate equations with switching control. We first establish the observability inequality for measurable subsets in time for such coupled system, and then by the HUM method to obtain the null controllability. Next, we investigate the null controllability of such coupled system for segmented time intervals. Notably, these results are obtained through spectral inequalities rather than using the method of Carleman estimates. Such coupled systems with switching control, to the best of our knowledge, are among the first to discuss.

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带开关控制的耦合抛物线系统的无效可控性

本文重点研究两种耦合系统的空可控性，包括具有开关控制的退化和非退化方程。我们首先建立了这类耦合系统在时间上可测子集的可观测性不等式，然后通过 HUM 方法获得空可控性。接下来，我们研究了这种耦合系统在分段时间间隔内的空可控性。值得注意的是，这些结果是通过谱不等式而不是使用卡勒曼估计方法得到的。据我们所知，这种具有开关控制的耦合系统是首次讨论的问题之一。

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

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.