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

Camilo Garcia-Tenorio and Alain Vande Wouwer ()
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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

Mathematics, 2022, vol. 10, issue 20, 1-18

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.

Keywords: extended dynamic mode decomposition; Koopman operator; orthogonal polynomials; mathematical modeling; dynamic systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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