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

Folkestad, Carl and Pastor, Daniel and Mezic, Igor and Mohr, Ryan and Fonoberova, Maria and Burdick, Joel (2020) Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control. In: 2020 American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 3906-3913. ISBN 9781538682661. https://resolver.caltech.edu/CaltechAUTHORS:20200730-143942801

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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 non-linear 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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.23919/acc45564.2020.9147729DOIArticle
https://arxiv.org/abs/1911.08751arXivDiscussion Paper
ORCID:
AuthorORCID
Mezic, Igor0000-0002-2873-9013
Fonoberova, Maria0000-0001-5438-524X
Additional Information:© 2020 AACC. The authors would like to thank the four anonymous referees for their thoughtful comments that helped improve this manuscript. This work has been supported in part by Raytheon Company and the DARPA Physics of Artificial Intelligence program, HR00111890033. The first author is grateful for the support of the Aker Scholarship Foundation.
Funders:
Funding AgencyGrant Number
Raytheon CompanyUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)HR00111890033
Aker Scholarship FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20200730-143942801
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200730-143942801
Official Citation:C. Folkestad, D. Pastor, I. Mezic, R. Mohr, M. Fonoberova and J. Burdick, "Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control," 2020 American Control Conference (ACC), Denver, CO, USA, 2020, pp. 3906-3913, doi: 10.23919/ACC45564.2020.9147729
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104662
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:31 Jul 2020 14:42
Last Modified:31 Jul 2020 14:42

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