Nonlinear state and parameter estimation using derivative information: A Lie-Sobolev approach
Nonlinear state and parameter estimation using derivative information: A Lie-Sobolev approach
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DOI：
10.1016/j.compchemeng.2021.107369
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
Wentao Tang;P. Daoutidis
中科院分区：
文献类型：
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作者：
Wentao Tang;P. Daoutidis
非线性控制的实现依赖于系统模型的准确性，然而，这往往是由潜在的动态参数和结构的不确定性的限制。在本文中，我们提出了估计参数和状态的方法，其目的是在匹配的识别模型和真正的动态不仅在直接输出测量，即在L 2意义上，但也在高阶时间导数的输出信号，即在Sobolev意义上。提出了一种基于Lie-Sobolev梯度下降的自适应估计器和一种基于Lie-Sobolev滚动时域估计器（MHE），研究了它们的收敛性及其对输入输出线性化控制和模型预测控制的影响。通过数值算例和一个具有复杂动力学的反应堆，证明了Lie-Sobolev状态和参数估计在非线性过程中的优越性。
The implementation of nonlinear control depends on the accuracy of the system model, which, however, is often restricted by parametric and structural uncertainty in the underlying dynamics. In this paper, we propose methods of estimating parameters and states that aim at matching the identified model and the true dynamics not only in the direct output measurements, ie, in an L 2-sense, but also in the higher-order time derivatives of the output signals, ie, in a Sobolev sense. A Lie-Sobolev gradient descent-based observer-estimator and a Lie-Sobolev moving horizon estimator (MHE) are formulated, and their convergence properties and effects on input–output linearizing control and model predictive control (MPC) respectively are studied. Advantages of Lie-Sobolev state and parameter estimation in nonlinear processes are demonstrated by numerical examples and a reactor with complex dynamics.