Koopman based data-driven predictive control

TL;DR

This paper introduces a novel data-driven control method for nonlinear systems that combines Koopman operator theory with Willems' lemma, enabling offline learning and uncertainty quantification through Wasserstein distance, validated by neural network experiments.

Contribution

It presents a new control scheme integrating Koopman theory with data-driven methods for nonlinear systems, including a simulation framework that accounts for model uncertainty.

Findings

Effective control demonstrated on nonlinear systems.

Successful uncertainty quantification using Wasserstein distance.

Numerical experiments with Bayesian neural networks validate the approach.

Abstract

Sparked by the Willems' fundamental lemma, a class of data-driven control methods has been developed for LTI systems. At the same time, the Koopman operator theory attempts to cast a nonlinear control problem into a standard linear one albeit infinite-dimensional. Motivated by these two ideas, a data-driven control scheme for nonlinear systems is proposed in this work. The proposed scheme is compatible with most differential regressors enabling offline learning. In particular, the model uncertainty is considered, enabling a novel data-driven simulation framework based on Wasserstein distance. Numerical experiments are performed with Bayesian neural networks to show the effectiveness of both the proposed control and simulation scheme.