Self-tuning moving horizon estimation of nonlinear systems via physics-informed machine learning Koopman modeling

Abstract

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.