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

• Published in: arXiv.org
• Main Authors: Junker, Annika, Timmermann, Julia, Trächtler, Ansgar
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 14.01.2022
• Subjects: Approximation; Computer Science - Systems and Control; Control stability; Control systems design; Design engineering; Engineering; Mathematical analysis; Mathematics - Optimization and Control; Numerical methods; Observability (systems)
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2112.07983

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.