具有边界扰动的变系数多维波动方程的稳定性

The Stabilization of Variable Coefficient Multi-Dimensional Wave Equation with Boundary Disturbance

应用自抗扰控制方法研究了具有边界扰动的变系数多维波动方程的稳定性.首先,使用时变高增益观测器代替常数高增益观测器很好地解决了峰值问题;其次,应用半群理论得到了加变系数多维波动方程解的存在性和唯一性;最后,设计时变高增益观测器估计出边界扰动,并通过状态反馈将其抵消使得系统稳定.

This paper is concerned with the stabilization of variable coefficient multi-dimensional wave equation with boundary disturbance, and the active disturbance rejection control approach is adopted in investigation. Firstly, the time varying high gain observer is applied to the system instead of constant high gain observer, which deals with the peaking value problem effectively, Secondly, the existence and uniqueness of the solution of variable coefficient multi-dimension ware equation are verified by using the semigroup theory. Finally, a time varying high gain observer is used to estimate the boundary disturbance and offset it by a state feedback, which makes the system stable.