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This paper develops data-driven methods to identify eigenfunctions of the Koopman operator associated to a dynamical system and subspaces that are invariant under the operator.
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M. O. Williams, I. G. Kevrekidis, and C. W. Rowley, “A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition,” Journal of Nonlinear Science , vol. 25, no. 6, pp. 1307–1346, 2015
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S. L. Brunton, B. W. Brunton, J. L. Proctor, and J. N. Kutz, “Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control,” PLOS One , vol. 11, no. 2, pp. 1–19, 2016
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A. Surana, M. O. Williams, M. Morari, and A. Banaszuk, “Koopman operator framework for constrained state estimation,” in IEEE Conf. on Decision and Control , Melbourne, Australia, 2017, pp. 94–101
2017
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B. Kramer, P. Grover, P. Boufounos, S. Nabi, and M. Benosman, “Sparse sensing and DMD-based identification of flow regimes and bifurcations in complex flows,” SIAM Journal on Applied Dynamical Systems , vol. 16, no. 2, pp. 1164–1196, 2017
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M. Haseli and J. Cortés, “Efficient identification of linear evolutions in nonlinear vector fields: Koopman invariant subspaces,” in IEEE Conf. on Decision and Control , Nice, France, Dec. 2019, pp. 1746–1751
2019
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D. Bruder, C. D. Remy, and R. Vasudevan, “Nonlinear system identification of soft robot dynamics using Koopman operator theory,” in IEEE Int. Conf. on Robotics and Automation , Montreal, Canada, May 2019, pp. 6244–6250
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S. Peitz and S. Klus, “Koopman operator-based model reduction for switched-system control of PDEs,” Automatica , vol. 106, pp. 184–191, 2019
2019
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G. Mamakoukas, M. Castano, X. Tan, and T. Murphey, “Local Koopman operators for data-driven control of robotic systems,” in Robotics: Science and Systems , Freiburg, Germany, Jun. 2019
2019
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A. Alla and J. N. Kutz, “Nonlinear model order reduction via dynamic mode decomposition,” SIAM Journal on Scientific Computing , vol. 39, no. 5, pp. B778–B796, 2017
2017
Cited alongside, same era.
2017
Cited alongside, same era.
A. Sootla and D. Ernst, “Pulse-based control using Koopman operator under parametric uncertainty,” IEEE Transactions on Automatic Control , vol. 63, no. 3, pp. 791–796, 2017
2017
Cited alongside, same era.
M. S. Hemati, C. W. Rowley, E. A. Deem, and L. N. Cattafesta, “De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets,” Theoretical and Computational Fluid Dynamics , vol. 31, no. 4, pp. 349–368, 2017
2017
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S. L. Clainche and J. M. Vega, “Higher-order dynamic mode decomposition,” SIAM Journal on Applied Dynamical Systems , vol. 16, no. 2, pp. 882–925, 2017
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 , vol. 27, no. 10, p. 103111, 2017
2017
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N. Takeishi, Y. Kawahara, and T. Yairi, “Learning Koopman invariant subspaces for dynamic mode decomposition,” in Conference on Neural Information Processing Systems , 2017, pp. 1130–1140
2017
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M. Netto and L. Mili, “A robust data-driven Koopman Kalman filter for power systems dynamic state estimation,” IEEE Transactions on Power Systems , vol. 33, no. 6, pp. 7228–7237, 2018
2018
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H. Zhang, C. W. Rowley, E. A. Deem, and L. N. Cattafesta, “Online dynamic mode decomposition for time-varying systems,” SIAM Journal on Applied Dynamical Systems , vol. 18, no. 3, pp. 1586–1609, 2019
2019
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S. Anantharamu and K. Mahesh, “A parallel and streaming dynamic mode decomposition algorithm with finite precision error analysis for large data,” Journal of Computational Physics , vol. 380, pp. 355–377, 2019
2019
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M. Haseli and J. Cortés, “Approximating the Koopman operator using noisy data: noise-resilient extended dynamic mode decomposition,” in American Control Conference , Philadelphia, PA, Jul. 2019, pp. 5499–5504
2019
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E. Yeung, S. Kundu, and N. Hodas, “Learning deep neural network representations for Koopman operators of nonlinear dynamical systems,” in American Control Conference , Philadelphia, PA, Jul. 2019, pp. 4832–4839
2019
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S. E. Otto and C. W. Rowley, “Linearly recurrent autoencoder networks for learning dynamics,” SIAM Journal on Applied Dynamical Systems , vol. 18, no. 1, pp. 558–593, 2019
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M. Korda and I. Mezić, “Optimal construction of Koopman eigenfunctions for prediction and control,” 2019. [Online]. Available: https://hal.archives-ouvertes.fr/hal-02278835
2019
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2019
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A. Mauroy and J. Goncalves, “Koopman-based lifting techniques for nonlinear systems identification,” IEEE Transactions on Automatic Control , vol. 65, no. 6, pp. 2550–2565, 2020
2020
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2020
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M. L. Castaño, A. Hess, G. Mamakoukas, T. Gao, T. Murphey, and X. Tan, “Control-oriented modeling of soft robotic swimmer with Koopman operators,” in IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) , 2020, pp. 1679–1685
2020
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E. Qian, B. Kramer, B. Peherstorfer, and K. Willcox, “Lift & learn: Physics-informed machine learning for large-scale nonlinear dynamical systems,” Physica D: Nonlinear Phenomena , vol. 406, p. 132401, 2020
2020
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M. Korda and I. Mezic, “Optimal construction of Koopman eigenfunctions for prediction and control,” IEEE Transactions on Automatic Control , 2020, to appear
2020
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