带边界非线性干扰的反稳定波方程的镇定

Stabilization for an anti-stable wave equation with boundary nonlinear disturbance

本文研究了一类具有边界控制匹配非线性干扰的反稳定波动方程的镇定问题.本文只用了两个量测,构造了一个无限维干扰估计器来实时估计状态和总干扰,该估计器既不要求干扰的导数有界,也不需要高增益.基于估计的总干扰和估计的状态,本文设计了输出反馈控制律稳定原系统.此外,本文还证明了闭环系统的其他状态是有界的.为了说明理论结果,下文给出了一些数值模拟.

We study stabilization for an anti-stable wave equation with boundary control matched interior uncertainty and external disturbance.Only two measurements are adopted.An infinite-dimensional disturbance estimator is constructed to estimate the state and total disturbance in real time,which does not presume the derivative of the disturbance to be bounded and recur to the high gain as usual.Based on the estimated total disturbance and estimated state,an output feedback control law is designed.Moreover,the other states of the closed-loop system are proved to be bounded.Some numerical simulations are presented for illustrating theoretical results.