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Nonlinearity presents a significant challenge in problems involving dynamical systems, prompting the exploration of various linearization techniques, including the well-known Carleman Linearization.
“Hamiltonian systems and transformation in Hilbert space”
Bernard Koopman · 1931
Earlier work this paper cites.
“Application de la théorie des équations intégrales linéaires aux systèmes d’équations différentielles non linéaires”, 1932
Torsten Carleman · 1932
Earlier work this paper cites.
“Dynamical systems of continuous spectra”
Bernard Koopman and J Neumann · 1932
Earlier work this paper cites.
“Dynamical Properties of Truncated Wiener-Hermite Expansions”
Steven Orszag and LR Bissonnette · 1967
Earlier work this paper cites.
“Estimating the domain of attraction of nonlinear feedback systems”
Kenneth Loparo and Gilmer Blankenship · 1978
Earlier work this paper cites.
“Lotka-Volterra equation and replicator dynamics: a two-dimensional classification”
Immanuel Bomze · 1983
Earlier work this paper cites.
“Spectral methods in MATLAB”
Lloyd Trefethen · 2000
Earlier work this paper cites.
“Spectral properties of dynamical systems, model reduction and decompositions”
Igor Mezić · 2005
Earlier work this paper cites.
“Carleman linearization for control and for state and disturbance estimation of nonlinear dynamical processes”
Andreas Rauh, Johanna Minisini and Harald Aschemann · 2009
Earlier work this paper cites.
“Spectral analysis of nonlinear flows”
Clarence Rowley et al · 2009
Earlier work this paper cites.
“Dynamic mode decomposition of numerical and experimental data”
Peter Schmid · 2010
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“Spectral methods: algorithms, analysis and applications”
Jie Shen, Tao Tang and Li-Lian Wang · 2011
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“Fast moving horizon estimation of nonlinear processes via Carleman linearization”
Negar Hashemian and Antonios Armaou · 2015
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“Extending data-driven Koopman analysis to actuated systems”
Matthew Williams et al · 2016
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“Explicit error bounds for Carleman linearization”
Marcelo Forets and Amaury Pouly · 2017
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“Variable projection methods for an optimized dynamic mode decomposition”
Travis Askham and J Kutz · 2018
“Applications of Koopman mode analysis to neural networks”
Iva Manojlović et al · 2020
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“Koopman operator in systems and control”
Alexandre Mauroy, Y Susuki and I Mezić · 2020
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“Error bounds for Carleman linearization of general nonlinear systems”
Arash Amini, Qiyu Sun and Nader Motee · 2021
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“Modern Koopman theory for dynamical systems”
Steven Brunton, Marko Budišić, Eurika Kaiser and J Kutz · 2021
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“Efficient quantum algorithm for dissipative nonlinear differential equations”
Jin-Peng Liu et al · 2021
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Bian Li, Yue Yu and Xiu Yang · 2022
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