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

TL;DR

This paper introduces a physics-informed machine learning approach using Koopman models for nonlinear systems, enabling efficient self-tuning moving horizon estimation that adapts online without re-training neural networks.

Contribution

It presents a novel Koopman-based estimation method combining physics-informed neural networks for noise and lifting functions, improving online adaptability and computational efficiency.

Findings

Effective in simulated chemical process

Achieves real-time estimation with adaptive tuning

Outperforms traditional methods in accuracy

Abstract

In this paper, 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 two neural networks account for the nonlinear lifting functions for Koopman modeling and describing system noise distributions, respectively. Accordingly, a stochastic linear Koopman model is established in the lifted space to forecast the dynamic behavior 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 pre-trained noise characterization network at each sampling instant. The proposed estimation scheme is computationally efficient because only convex optimization is involved 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.