Boundary controllability for a 1D degenerate parabolic equation with a Robin boundary condition

IF 1.8 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Mathematics of Control Signals and Systems Pub Date : 2024-04-06 DOI:10.1007/s00498-024-00383-8

引用次数: 0

Abstract

In this paper, we prove the null controllability of a one-dimensional degenerate parabolic equation with a weighted Robin boundary condition at the left endpoint, where the potential has a singularity. We use some results from the singular Sturm–Liouville theory to show the well-posedness of our system. We obtain a spectral decomposition of a degenerate parabolic operator with Robin conditions at the endpoints, we use Fourier–Dini expansions and the moment method introduced by Fattorini and Russell to prove the null controllability and to obtain an upper estimate of the cost of controllability. We also get a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type.

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具有罗宾边界条件的一维退化抛物方程的边界可控性

摘要本文证明了一个一维退化抛物方程的空可控性，该方程在左端点具有加权罗宾边界条件，其势能具有奇异性。我们利用奇异 Sturm-Liouville 理论的一些结果来证明我们的系统具有良好的拟合性。我们得到了一个在端点具有罗宾条件的退化抛物线算子的谱分解，并利用傅立叶-迪尼展开以及法托里尼和罗素引入的矩方法证明了空可控性，并得到了可控性代价的上估计值。我们还利用指数型解析函数的表示定理得到了可控性成本的下限估计。

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

Mathematics of Control Signals and Systems 工程技术-工程：电子与电气

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematics of Control, Signals, and Systems (MCSS) is an international journal devoted to mathematical control and system theory, including system theoretic aspects of signal processing. Its unique feature is its focus on mathematical system theory; it concentrates on the mathematical theory of systems with inputs and/or outputs and dynamics that are typically described by deterministic or stochastic ordinary or partial differential equations, differential algebraic equations or difference equations. Potential topics include, but are not limited to controllability, observability, and realization theory, stability theory of nonlinear systems, system identification, mathematical aspects of switched, hybrid, networked, and stochastic systems, and system theoretic aspects of optimal control and other controller design techniques. Application oriented papers are welcome if they contain a significant theoretical contribution.