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We develop a novel lifting technique for nonlinear system identification based on the framework of the Koopman operator.
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P. J. Schmid, “Dynamic mode decomposition of numerical and experimental data,” Journal of Fluid Mechanics , vol. 656, pp. 5–28, 2010
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A. Mauroy and J. Goncalves, “Linear identification of nonlinear systems: A lifting technique based on the Koopman operator,” in Proceedings of the 55th IEEE Conference on Decision and Control , 2016, pp. 6500–6505
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S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Sparse identification of nonlinear dynamics with control (SINDYc),” in Proceedings of the IFAC Conference , vol. 49, no. 18, 2016, pp. 710–715
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J. L. Proctor, S. L. Brunton, and J. N. Kutz, “Dynamic mode decomposition with control,” SIAM Journal on Applied Dynamical Systems , vol. 15, no. 1, pp. 142–161, 2016
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2011
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Y. Zhang, J. Yang, and Y. W., YALL1: Your ALgorithms for L1 , yall1.blogs.rice.edu, 2011
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M. Budišić, R. Mohr, and I. Mezić, “Applied Koopmanism,” Chaos , vol. 22, no. 4, pp. 047 510–047 510, 2012
2012
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P. Van Overschee and B. De Moor, Subspace identification for linear systems: Theory—Implementation—Applications . Springer Science & Business Media, 2012
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Y. Lan and I. Mezić, “Linearization in the large of nonlinear systems and Koopman operator spectrum,” Physica D , vol. 242, pp. 42–53, 2013
2013
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J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz, “On dynamic mode decomposition: Theory and applications,” Journal of Computational Dynamics , vol. 1, no. 2, pp. 391 – 421, December 2014
2014
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Y. Susuki and I. Mezić, “Nonlinear Koopman modes and power system stability assessment without models,” IEEE Transactions On Power Systems , vol. 29, no. 2, pp. 899–907, March 2014
2014
Cited alongside, same era.
2014
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W. Pan, F. Menolascina, and G.-B. Stan, “Online model selection for synthetic gene networks,” in Proceedings of the 55th IEEE Conference on Decision and Control . IEEE, 2016, pp. 776–782
2016
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N. M. Mangan, S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Inferring biological networks by sparse identification of nonlinear dynamics,” IEEE Transactions on Molecular, Biological and Multi-Scale Communications , vol. 2, no. 1, pp. 52–63, 2016
2016
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A. Mauroy and A. Sootla, “Geometric properties of isostables and basins of attraction of monotone systems,” 2017, to appear in IEEE Transactions on Automatic Control
2017
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2017
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H. Arbabi and I. Mezić, “Ergodic theory, Dynamic Mode Decomposition and computation of spectral properties of the Koopman operator,” SIAM Journal on Applied Dynamical Systems , vol. 16, no. 4, pp. 2096–2126, 2017
2017
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2017
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2017
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Q. Li, F. Dietrich, E. M. Bollt, and I. G. Kevrekidis, “Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator,” Chaos: An Interdisciplinary Journal of Nonlinear Science , vol. 27, p. 103111, 2017
2017
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M. Korda and I. Mezić, “Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control,” Automatica , vol. 93, pp. 149–160, 2018
2018
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2018
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M. Korda and I. Mezić, “On convergence of extended dynamic mode decomposition to the Koopman operator,” Journal of Nonlinear Science , vol. 28, no. 2, pp. 687–710, 2018
2018
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L. P. Proctor, S. L. Brunton, and J. N. Kutz, “Generalizing Koopman operator theory to allow for inputs and control,” SIAM Journal on Applied Dynamical Systems , vol. 17, no. 1, pp. 909–930, 2018
2018
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