Data-Driven Models for Control Engineering Applications Using the Koopman Operator

TL;DR

This paper explores how data-driven Koopman operator approximation methods, specifically EDMD, can be effectively used in control engineering for modeling, analysis, and control design, demonstrated through simulations and experiments.

Contribution

It demonstrates the practical application of EDMD for control engineering, showing its effectiveness in modeling, stability analysis, and control design on real systems.

Findings

EDMD provides accurate linear models of nonlinear systems.

The models reflect key properties like stability and controllability.

Experimental results confirm suitability for control design processes.

Abstract

Within this work, we investigate how data-driven numerical approximation methods of the Koopman operator can be used in practical control engineering applications. We refer to the method Extended Dynamic Mode Decomposition (EDMD), which approximates a nonlinear dynamical system as a linear model. This makes the method ideal for control engineering applications, because a linear system description is often assumed for this purpose. Using academic examples, we simulatively analyze the prediction performance of the learned EDMD models and show how relevant system properties like stability, controllability, and observability are reflected by the EDMD model, which is a critical requirement for a successful control design process. Subsequently, we present our experimental results on a mechatronic test bench and evaluate the applicability to the control engineering design process. As a result, the investigated methods are suitable as a low-effort alternative for the design steps of model building and adaptation in the classical model-based controller design method.