IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3859-d945500.html
   My bibliography  Save this article

A Matlab Toolbox for Extended Dynamic Mode Decomposition Based on Orthogonal Polynomials and p-q Quasi-Norm Order Reduction

Author

Listed:
  • Camilo Garcia-Tenorio

    (Systems, Estimation, Control and Optimization (SECO), Université de Mons, 7000 Mons, Belgium)

  • Alain Vande Wouwer

    (Systems, Estimation, Control and Optimization (SECO), Université de Mons, 7000 Mons, Belgium)

Abstract

Extended Dynamic Mode Decomposition (EDMD) allows an approximation of the Koopman operator to be derived in the form of a truncated (finite dimensional) linear operator in a lifted space of (nonlinear) observable functions. EDMD can operate in a purely data-driven way using either data generated by a numerical simulator of arbitrary complexity or actual experimental data. An important question at this stage is the selection of basis functions to construct the observable functions, which in turn is determinant of the sparsity and efficiency of the approximation. In this study, attention is focused on orthogonal polynomial expansions and an order-reduction procedure called p-q quasi-norm reduction. The objective of this article is to present a Matlab library to automate the computation of the EDMD based on the above-mentioned tools and to illustrate the performance of this library with a few representative examples.

Suggested Citation

  • Camilo Garcia-Tenorio & Alain Vande Wouwer, 2022. "A Matlab Toolbox for Extended Dynamic Mode Decomposition Based on Orthogonal Polynomials and p-q Quasi-Norm Order Reduction," Mathematics, MDPI, vol. 10(20), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3859-:d:945500
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3859/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3859/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Camilo Garcia-Tenorio & Gilles Delansnay & Eduardo Mojica-Nava & Alain Vande Wouwer, 2021. "Trigonometric Embeddings in Polynomial Extended Mode Decomposition—Experimental Application to an Inverted Pendulum," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    2. Steven L Brunton & Bingni W Brunton & Joshua L Proctor & J Nathan Kutz, 2016. "Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-19, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Zhong & Chen, Xiaofang & Liu, Jinping & Cen, Lihui & Gui, Weihua, 2024. "Learning model predictive control of nonlinear systems with time-varying parameters using Koopman operator," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    2. Nassir Cassamo & Jan-Willem van Wingerden, 2020. "On the Potential of Reduced Order Models for Wind Farm Control: A Koopman Dynamic Mode Decomposition Approach," Energies, MDPI, vol. 13(24), pages 1-21, December.
    3. Oster, Matthew R. & King, Ethan & Bakker, Craig & Bhattacharya, Arnab & Chatterjee, Samrat & Pan, Feng, 2023. "Multi-level optimization with the koopman operator for data-driven, domain-aware, and dynamic system security," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    4. Riccardo Colantuono & Riccardo Colantuono & Massimiliano Mazzanti & Michele Pinelli, 2023. "Aviation and the EU ETS: an overview and a data-driven approach for carbon price prediction," SEEDS Working Papers 0123, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Feb 2023.
    5. Jamiree Harrison & Enoch Yeung, 2021. "Stability Analysis of Parameter Varying Genetic Toggle Switches Using Koopman Operators," Mathematics, MDPI, vol. 9(23), pages 1-25, December.
    6. Mallen, Alex T. & Lange, Henning & Kutz, J. Nathan, 2024. "Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties," International Journal of Forecasting, Elsevier, vol. 40(3), pages 859-868.
    7. Keita Hara & Masaki Inoue, 2021. "Gain-Preserving Data-Driven Approximation of the Koopman Operator and Its Application in Robust Controller Design," Mathematics, MDPI, vol. 9(9), pages 1-18, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3859-:d:945500. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.