Data-driven Koopman Operator-based Prediction and Control Using Model Averaging

TL;DR

This paper introduces a data-driven approach for modeling and control of nonlinear dynamics using Koopman operators combined with Bayesian model averaging, enhancing accuracy across diverse operating conditions.

Contribution

It proposes a novel ensemble method that leverages neural network feature extraction and Bayesian model averaging to improve Koopman operator-based predictions.

Findings

Improved modeling accuracy over single Koopman models.

Effective handling of unseen data and diverse operating points.

Enhanced control performance through model ensemble.

Abstract

This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately reconstruct unknown dynamics from data and perform different decision-making tasks, mainly due to its infinite dimensionality and difficulty of finding invariant subspaces. We utilize ideas from a Bayesian inference-based model averaging technique to devise a data-driven method that first populates multiple Koopman models starting with a feature extraction using neural networks and then computes point estimates of the posterior of predicted variables. Although each model in the ensemble is not likely to be accurate enough for a wide range of operating points or unseen data, the proposed weighted linear embedding model combines the outputs of model ensemble aiming at compensating the modeling error of each model so that the overall performance will be improved.