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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
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    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.
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