Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control

TL;DR

This paper introduces a new learning framework that constructs Koopman eigenfunctions from experimental data to linearize nonlinear dynamics, enabling improved prediction and control using linear methods.

Contribution

It is the first to use Koopman eigenfunctions as lifting functions for EDMD, enhancing nonlinear system modeling and control.

Findings

Significantly improved state prediction accuracy.

Enhanced closed-loop trajectory tracking performance.

Effective linear control of nonlinear systems.

Abstract

This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the associated Koopman operator. We then exploit the learned Koopman eigenfunctions to learn a lifted linear state-space model. To the best of our knowledge, our method is the first to utilize Koopman eigenfunctions as lifting functions for EDMD-based methods. We demonstrate the performance of the framework in state prediction and closed loop trajectory tracking of a simulated cart pole system. Our method is able to significantly improve the controller performance while relying on linear control methods to do nonlinear control.