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The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data.
Hamiltonian systems and transformation in hilbert space
Bernard O Koopman · 1931
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Dynamical systems of continuous spectra
B. O. Koopman and J. von Neumann · 1932
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Detecting strange attractors in turbulence
Floris Takens · 1981
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Generalized eigenproblem algorithms and software for algebraic Riccati equations
William F Arnold and Alan J Laub · 1984
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Nonparametric identification of nonlinear time series: projections
Dag Tjøstheim and Bjørn H Auestad · 1994
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System identification
Lennart Ljung · 1998
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Constrained model predictive control: Stability and optimality
David Q Mayne, James B Rawlings, Christopher V Rao, and Pierre OM Scokaert · 2000
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Spectral methods in MATLAB
Lloyd N Trefethen · 2000
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Flow control: new challenges for a new renaissance
Thomas R Bewley · 2001
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DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms
Thomas R Bewley, Parviz Moin, and Roger Temam · 2001
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Balanced model reduction via the proper orthogonal decomposition
Karen Willcox and Jaime Peraire · 2002
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A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
Bernd R Noack, Konstantin Afanasiev, Marek Morzynski, Gilead Tadmor, and Frank Thiele · 2003
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Comparison of systems with complex behavior
Igor Mezić and Andrzej Banaszuk · 2004
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Model reduction for fluids, using balanced proper orthogonal decomposition
CW Rowley · 2005
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Spectral properties of dynamical systems, model reduction and decompositions
Igor Mezić · 2005
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Experimental feedback control of flow-induced cavity tones
Randolph H Cabell, Michael A Kegerise, David E Cox, and Gary P Gibbs · 2006
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A linear systems approach to flow control
John Kim and Thomas R Bewley · 2007
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Control and system identification of a separated flow
Shao-Ching Huang and John Kim · 2008
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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
Peter J Schmid · 2010
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Physics and control of wall turbulence for drag reduction
John Kim · 2011
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Applications of the dynamic mode decomposition
Peter J Schmid, L Li, MP Juniper, and O Pust · 2011
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Nonlinear model predictive control
Lars Grüne and Jürgen Pannek · 2011
Cited alongside, same era.
Turbulence, coherent structures, dynamical systems and symmetry
Philip Holmes, John L Lumley, Gal Berkooz, and Clarence Rowley · 2012
Cited alongside, same era.
A physics-based approach to flow control using system identification
Aurelien Hervé, Denis Sipp, Peter J Schmid, and Manuel Samuelides · 2012
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Applied koopmanism a)
Marko Budišić, Ryan Mohr, and Igor Mezić · 2012
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On the use of fourier averages to compute the global isochrons of (quasi) periodic dynamics
Alexandre Mauroy and Igor Mezić · 2012
Cited alongside, same era.
Dynamic-mode decomposition based analysis of shear coaxial jets with and without transverse acoustic driving
Jia-Chen Hua, Gemunu H Gunaratne, Douglas G Talley, James R Gord, and Sukesh Roy · 2016
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Generalizing Koopman theory to allow for inputs and control
Joshua L Proctor, Steven L Brunton, and J Nathan Kutz · 2016
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Extending data-driven Koopman analysis to actuated systems
Matthew O. Williams, Maziar S. Hemati, Scott T. M. Dawson, Ioannis G. Kevrekidis, and Clarence W. Rowley · 2016
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Dynamic mode decomposition with control
Joshua L Proctor, Steven L Brunton, and J Nathan Kutz · 2016
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Linear observer synthesis for nonlinear systems using Koopman operator framework
Amit Surana and Andrzej Banaszuk · 2016
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Low-dimensional modelling of high-reynolds-number shear flows incorporating constraints from the navier–stokes equation
Maciej J Balajewicz, Earl H Dowell, and Bernd R Noack · 2013
Cited alongside, same era.
Reduced-order unsteady aerodynamic models at low reynolds numbers
Steven L Brunton, Clarence W Rowley, and David R Williams · 2013
Cited alongside, same era.
Analysis of fluid flows via spectral properties of the Koopman operator
Igor Mezić · 2013
Cited alongside, same era.
Koopman-mode decomposition of the cylinder wake
Shervin Bagheri · 2013
Cited alongside, same era.
Mathematical control theory: deterministic finite dimensional systems
Eduardo D Sontag · 2013
Cited alongside, same era.
Reduced-order representation of near-wall structures in the late transitional boundary layer
Taraneh Sayadi, Peter J Schmid, Joseph W Nichols, and Parviz Moin · 2014
Cited alongside, same era.
Global stability analysis using the eigenfunctions of the Koopman operator
Alexandre Mauroy and Igor Mezić · 2016
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Koopman operator-based model reduction for switched-system control of pdes
Sebastian Peitz and Stefan Klus · 2017
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Quasi-periodic intermittency in oscillating cylinder flow
Bryan Glaz, Igor Mezić, Maria Fonoberova, and Sophie Loire · 2017
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An optimal control formulation of pulse-based control using koopman operator
Aivar Sootla, Alexandre Mauroy, and Damien Ernst · 2017
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Koopman-based lifting techniques for nonlinear systems identification
Alexandre Mauroy and Jorge Goncalves · 2017
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Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator
Hassan Arbabi and Igor Mezic · 2017
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On convergence of extended dynamic mode decomposition to the Koopman operator
Milan Korda and Igor Mezić · 2017
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Data-driven spectral analysis of the Koopman operator
Milan Korda, Mihai Putinar, and Igor Mezić · 2017
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Koopman operator spectrum and data analysis
Igor Mezić · 2017
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Data-driven spectral decomposition and forecasting of ergodic dynamical systems
Dimitrios Giannakis · 2017
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Study of dynamics in post-transient flows using Koopman mode decomposition
Hassan Arbabi and Igor Mezić · 2017
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Learning deep neural network representations for koopman operators of nonlinear dynamical systems
Enoch Yeung, Soumya Kundu, and Nathan Hodas · 2017
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Learning koopman invariant subspaces for dynamic mode decomposition
Naoya Takeishi, Yoshinobu Kawahara, and Takehisa Yairi · 2017
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Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
Milan Korda and Igor Mezić · 2018
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Controlling nonlinear pdes using low-dimensional bilinear approximations obtained from data
Sebastian Peitz · 2018
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