An Efficient Implementation of Backstepping Observers for Time-Varying Parabolic PDEs
An Efficient Implementation of Backstepping Observers for Time-Varying Parabolic PDEs
复制标题
时变抛物线偏微分方程反步观测器的有效实现
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
A. Kugi
中科院分区：
文献类型：
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作者：
L. Jadachowski;T. Meurer;A. Kugi
摘要针对具有时变参数和空变参数的一维扩散-反应系统，提出了一种新的基于反推的状态观测器。为此，隐式制定的积分核，这是从应用程序的反推过程中离散化的空间和近似的复合梯形规则。这导致在一个系统的一阶常微分方程的逐点显式的时间演化的backstepping内核。所得到的系统的常微分方程数值求解应用向后欧拉方法，大大减少了计算时间相比，通常应用的逐次逼近法。所提出的方法对计算时间和观测器误差收敛的影响进行了评估，通过数值模拟。
Abstract A new computationally efficient implementation of the backstepping-based state observer is considered for a 1-dimensional diffusion-reaction system with spatially and time varying parameters. For this, the implicit formulation for the integral kernel, which results from the application of the backstepping procedure is discretized in space and approximated by means of the composite trapezoidal rule. This results in a system of first-order ordinary differential equations governing the pointwise explicit-in-time evolution of the backstepping-kernel. The resulting system of ODEs is numerically solved by applying the backward Euler method, which drastically reduces the computing time compared to the usually applied method of successive approximation. The impact of the proposed method on the computing time and on the observer error convergence is evaluated by means of numerical simulations.