具有动态边界控制的弹性板的多项式稳定性

Q3 Engineering

IFAC-PapersOnLine Pub Date : 2025-01-01 DOI:10.1016/j.ifacol.2025.08.096

Yanan Sun , Qiong Zhang

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引用次数: 0

摘要

本文研究了弹性薄板的边界反馈稳定化问题，其中薄板的一部分边界被夹紧，剩余的自由部分附着在刚体上。边界反馈控制应用于自由边界。考虑到域的边界可能存在角点，我们引入了一个适当的抽象框架来分析域的适定性和估计解。当几何控制条件（GCC）成立时，我们证明了多项式能量衰减率为t-1/2。对于GCC不成立的情况，我们在矩形域上分析系统，只对一条边施加控制，并获得较慢的衰减率t-1/3。

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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Polynomial Stability of an Elastic Plate with Dynamical Boundary Control

This work studies the boundary feedback stabilization for an elastic thin plate, where one part of its boundary is clamped and the remaining free part is attached to a rigid body. The boundary feedback controls are applied to the free boundary. Given that the boundary of the domain may have corners, we introduce a proper abstract framework to analyze the well-posedness and estimate the resolvent. When the geometric control condition (GCC) holds, we prove a polynomial energy decay rate of t^-1/2. For cases where GCC does not hold, we analyze the system on a rectangular domain with control applied to only one edge and obtain a slower decay rate t^-1/3.

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来源期刊

IFAC-PapersOnLine Engineering-Control and Systems Engineering

CiteScore

1.70

自引率

0.00%

发文量

1122

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