A Matlab Toolbox for Extended Dynamic Mode Decomposition Based on Orthogonal Polynomials and p-q Quasi-Norm Order Reduction
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Published:2022-10-18
Issue:20
Volume:10
Page:3859
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ISSN:2227-7390
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Container-title:Mathematics
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language:en
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Short-container-title:Mathematics
Author:
Garcia-Tenorio CamiloORCID,
Vande Wouwer AlainORCID
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.
Funder
Belgium Wallonia Research BeWaRe
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference30 articles.
1. A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
2. System Identification: Theory for the User;Ljung,1999
3. Optimal Estimation of Dynamic Systems;John,2004
4. CHAPTER 40—Multivariate autoregressive models;Penny,2007
5. Stochastic Finite Elements: A Spectral Approach;Roger,2003
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