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We develop a data-driven, model-free approach for the optimal control of the dynamical system.
B. O. Koopman, “Hamiltonian systems and transformation in hilbert space,” Proceedings of the national academy of sciences of the united states of america , vol. 17, no. 5, p. 315, 1931
1931
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I. Mezić, “Spectral properties of dynamical systems, model reductions and decompositions,” Nonlinear Dynamics , 2005
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U. Vaidya and P. G. Mehta, “Lyapunov measure for almost everywhere stability,” IEEE Transactions on Automatic Control , vol. 53, pp. 307–323, 2008
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U. Vaidya, P. Mehta, and U. Shanbhag, “Nonlinear stabilization via control Lyapunov measure,” IEEE Transactions on Automatic Control , vol. 55, pp. 1314–1328, 2010
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Y. Susuki and I. Mezic, “Nonlinear koopman modes and coherency identification of coupled swing dynamics,” IEEE Transactions on Power Systems , vol. 26, no. 4, pp. 1894–1904, 2011
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M. Budisic, R. Mohr, and I. Mezic, “Applied koopmanism,” Chaos , vol. 22, pp. 047 510–32, 2012
2012
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A. Raghunathan and U. Vaidya, “Optimal stabilization using lyapunov measures,” IEEE Transactions on Automatic Control , vol. 59, no. 5, pp. 1316–1321, 2014
2014
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2014
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2014
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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
2015
Cited alongside, same era.
2015
Cited alongside, same era.
A. Surana and A. Banaszuk, “Linear observer synthesis for nonlinear systems using koopman operator framework,” in Proceedings of IFAC Symposium on Nonlinear Control Systems , Monterey, California, 2016
2016
Cited alongside, same era.
A. Mauroy and I. Mezić, “Global stability analysis using the eigenfunctions of the koopman operator,” IEEE Transactions on Automatic Control , vol. 61, no. 11, pp. 3356–3369, 2016
2016
Cited alongside, same era.
R. S. Sutton and A. G. Barto, Reinforcement learning: An introduction . MIT press, 2018
2018
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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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B. Lusch, J. N. Kutz, and S. L. Brunton, “Deep learning for universal linear embeddings of nonlinear dynamics,” Nature communications , vol. 9, no. 1, pp. 1–10, 2018
2018
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2018
Later among the works it cites.
P. You, J. Pang, and E. Yeung, “Deep koopman controller synthesis for cyber-resilient market-based frequency regulation,” IFAC-PapersOnLine , vol. 51, no. 28, pp. 720–725, 2018
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2016
Cited alongside, same era.
M. O. Williams, M. S. Hemati, S. T. Dawson, I. G. Kevrekidis, and C. W. Rowley, “Extending data-driven koopman analysis to actuated systems,” IFAC-PapersOnLine , vol. 49, no. 18, pp. 704–709, 2016
2016
Cited alongside, same era.
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
2016
Cited alongside, same era.
2017
Cited alongside, same era.
2017
Cited alongside, same era.
2018
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B. Huang, X. Ma, and U. Vaidya, “Feedback stabilization using koopman operator,” in 2018 IEEE Conference on Decision and Control (CDC) . IEEE, 2018, pp. 6434–6439
2018
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E. Yeung, S. Kundu, and N. Hodas, “Learning deep neural network representations for koopman operators of nonlinear dynamical systems,” in 2019 American Control Conference (ACC) . IEEE, 2019, pp. 4832–4839
2019
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X. Ma, B. Huang, and U. Vaidya, “Optimal quadratic regulation of nonlinear system using koopman operator,” in 2019 American Control Conference (ACC) . IEEE, 2019, pp. 4911–4916
2019
Later among the works it cites.
E. Kaiser, J. N. Kutz, and S. L. Brunton, “Data-driven approximations of dynamical systems operators for control,” in The Koopman Operator in Systems and Control . Springer, 2020, pp. 197–234
2020
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