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This paper tackles the data-driven approximation of unknown dynamical systems using Koopman-operator methods.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
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Dynamical systems of continuous spectra
B. O. Koopman and J. V. Neumann · 1932
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Eigenvalues of the difference and product of projections
W. N. Anderson Jr, E. J. Harner, and G. E. Trapp · 1985
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Numerical Linear Algebra
L. N. Trefethen and D. Bau · 1997
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Spectral properties of dynamical systems, model reduction and decompositions
I. Mezić · 2005
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Distributed algorithms for reaching consensus on general functions
J. Cortés · 2008
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Optimization algorithms on matrix manifolds
P. A. Absil, R. Mahony, and R. Sepulchre · 2009
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Spectral analysis of nonlinear flows
C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D. S. Henningson · 2009
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Dynamic mode decomposition of numerical and experimental data
P. J. Schmid · 2010
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Applied Koopmanism
M. Budišić, R. Mohr, and I. Mezić · 2012
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The Hopf bifurcation and its applications , volume 19
J. E. Marsden and M. McCracken · 2012
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On dynamic mode decomposition: theory and applications
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz · 2014
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A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition
M. O. Williams, I. G. Kevrekidis, and C. W. Rowley · 2015
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Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
S. T. M. Dawson, M. S. Hemati, M. O. Williams, and C. W. Rowley · 2016
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On the numerical approximation of the Perron-Frobenius and Koopman operator
S. Klus, P. Koltai, and C. Schütte · 2016
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Global stability analysis using the eigenfunctions of the Koopman operator
A. Mauroy and I. Mezić · 2016
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Learning Koopman invariant subspaces for dynamic mode decomposition
N. Takeishi, Y. Kawahara, and T. Yairi · 2017
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A class of logistic functions for approximating state-inclusive Koopman operators
C. A. Johnson and E. Yeung · 2018
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Deep learning for universal linear embeddings of nonlinear dynamics
Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
S. Klus, F. Nüske, S. Peitz, J. H. Niemann, C. Clementi, and C. Schütte · 2020
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Optimal construction of Koopman eigenfunctions for prediction and control
M. Korda and I. Mezic · 2020
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Prediction accuracy of dynamic mode decomposition
H. Lu and D. M. Tartakovsky · 2020
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S. H. Son, A. Narasingam, and J. S. Kwon · 2020
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Data-driven discovery of Koopman eigenfunctions for control
E. Kaiser, J. N. Kutz, and S. L. Brunton · 2021
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B. Lusch, J. N. Kutz, and S. L. Brunton · 2018
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Approximating the Koopman operator using noisy data: noise-resilient extended dynamic mode decomposition
M. Haseli and J. Cortés · 2019
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Local Koopman operators for data-driven control of robotic systems
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Finite-data error bounds for Koopman-based prediction and control
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Sparsity-promoting algorithms for the discovery of informative Koopman-invariant subspaces
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