In this paper, we are concerned with dynamic stabilisation for a one-dimensional Euler–Bernoulli beam equation with boundary moment control and matched nonlinear uncertain disturbance. In the case of no disturbance, we show that a boundary feedback control law exponentially stabilises the system and Riesz basis generation holds for the closed-loop system. The well-posedness of the system in the sense of Salamon-Weiss, which is essentially important for the design of observer, is verified. We design an infinite-dimensional disturbance estimator, which doesn't need slow variation or high gain or boundedness of the derivation of the disturbance, to estimate the total disturbance. Based on the disturbance estimator, we design an output feedback control law. The Riesz basis generation and exponential stability of a couple system including the original equation is proved. Moreover, the boundedness of the closed-loop system is verified. Some numerical simulations are presented to illustrate the results.

在本文中，我们关注具有边界矩控制和匹配非线性不确定扰动的一维 Euler-Bernoulli 梁方程的动态稳定。在没有干扰的情况下，我们表明边界反馈控制律以指数方式稳定系统，并且 Riesz 基生成适用于闭环系统。验证了对观测器设计至关重要的Salamon-Weiss意义上的系统适定性。我们设计了一个无限维扰动估计器，它不需要缓慢变化或高增益或扰动推导的有界性来估计总扰动。基于扰动估计，我们设计了输出反馈控制律。证明了包含原方程的偶系统的Riesz基生成和指数稳定性。此外，验证了闭环系统的有界性。给出了一些数值模拟来说明结果。