带有扰动的一维波动方程的镇定

Stabilization of One-dimensional Wave Equation with Disturbance

研究了带有扰动的一维波动方程的镇定问题。首先,基于量测位移的加权平均来设计时变的扩张状态观测器对波动方程的干扰进行估计,然后在反馈环节中将干扰消除,最后利用算子半群理论和李雅普诺夫方法证明了闭环系统解的适定性和渐近稳定性,并通过数值模拟验证了文章的结论。

This paper is concerned with the stabilization of one-dimensional wave equation with disturbance. Firstly, the time varying gain observer based on weighted average of measurement displacement is applied to estimate the disturbance, and then the disturbance is eliminated in the feedback loop. Finally, the well-posedness and asymptotic stabilization of the closed-loop are proved by using operator semigroup theory and Lyapunov method. We also provide numerical simulations which demonstrate the results of this paper.