Output feedback stabilization of an unstable wave equation with general corrupted boundary observation
Output feedback stabilization of an unstable wave equation with general corrupted boundary observation
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DOI：
10.1016/j.automatica.2014.10.016
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
Hongyinping Feng;B. Guo
中科院分区：
文献类型：
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作者：
Hongyinping Feng;B. Guo
考虑一类具有边界观测的不稳定波动方程在一般扰动下的边界输出反馈镇定问题。本文首次采用自抗扰控制方法对一个由偏微分方程描述的带有损坏输出反馈的系统进行镇定。该方法首先用一个相对独立的估计器估计扰动，然后在反馈回路中消除扰动。结果表明，所设计的控制律与无扰动系统的控制律基本相同。我们证明了在适当设计时变增益的情况下，由扰动估计器驱动的观测器是收敛的，并且闭环中的所有子系统在能量状态空间中是渐近稳定的。我们还提供了数值模拟，证明了收敛的结果，并强调了随时间变化的增益估计峰值降低的效果。
We consider boundary output feedback stabilization for an unstable wave equation with boundary observation subject to a general disturbance. We adopt for the first time the active disturbance rejection control approach to stabilization for a system described by the partial differential equation with corrupted output feedback. By the approach, the disturbance is first estimated by a relatively independent estimator; it is then canceled in the feedback loop. As a result, the control law can be designed almost as that for the system without disturbance. We show that with a time varying gain properly designed, the observer driven by the disturbance estimator is convergent, and that all subsystems in the closed-loop are asymptotically stable in the energy state space. We also provide numerical simulations which demonstrate the convergence results and underline the effect of the time varying gain estimator on peaking value reduction.