In this article, we propose a physics‐informed learning‐based Koopman modeling approach and present a Koopman‐based self‐tuning moving horizon estimation design for a class of nonlinear systems. Specifically, we train Koopman operators and two neural networks—the state lifting network and the noise characterization network—using both data and available physical information. The first network accounts for the nonlinear lifting functions for the Koopman model, while the second network characterizes the system noise distributions. Accordingly, a stochastic linear Koopman model is established in the lifted space to forecast the dynamic behaviors of the nonlinear system. Based on the Koopman model, a self‐tuning linear moving horizon estimation (MHE) scheme is developed. The weighting matrices of the MHE design are updated using the pretrained noise characterization network at each sampling instant. The proposed estimation scheme is computationally efficient, as only convex optimization needs to be solved during online implementation, and updating the weighting matrices of the MHE scheme does not require re‐training the neural networks. We verify the effectiveness and evaluate the performance of the proposed method via the application to a simulated chemical process.

中文翻译：

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通过物理学机器学习对非线性系统进行自整定移动视界估计 Koopman 建模


在本文中，我们提出了一种基于物理学的 Koopman 建模方法，并提出了一种基于考夫曼的自调谐移动水平估计设计，用于一类非线性系统。具体来说，我们使用数据和可用的物理信息来训练 Koopman 算子和两个神经网络——状态提升网络和噪声表征网络。第一个网络考虑了 Koopman 模型的非线性提升函数，而第二个网络描述了系统噪声分布的特征。因此，在升空中建立了随机线性 Koopman 模型来预测非线性系统的动力学行为。基于 Koopman 模型，开发了一种自调谐线性移动水平估计 （MHE） 方案。MHE 设计的加权矩阵在每个采样时刻使用预训练的噪声表征网络进行更新。所提出的估计方案在计算上是高效的，因为在在线实现过程中只需要解决凸优化，并且更新 MHE 方案的加权矩阵不需要重新训练神经网络。我们通过应用于模拟化学过程来验证所提出的方法的有效性并评估其性能。