The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of flexible mechanical systems. A linear feedback controller is proposed, and using an abstract formulation based on operator semigroup theory, we are able to prove the well-posedness and the stability of the closed-loop system. The performances of the proposed controller are illustrated by means of numerical simulations.

中文翻译：

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由柔性机器人产生的高阶偏微分方程系统的边界稳定

研究了通过边界控制来稳定四阶耦合偏微分方程系统的问题。所考虑的设置源自经典的 Euler-Bernoulli 梁模型，并构成了柔性机械系统的概括。提出了一种线性反馈控制器，并使用基于算子半群理论的抽象公式，证明了闭环系统的适定性和稳定性。所提出的控制器的性能通过数值模拟来说明。