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We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
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Principles and techniques of applied mathematics
Bernard Friedman · 1961
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An eigensystem realization algorithm for modal parameter identification and model reduction
J. N. Juang and R. S. Pappa · 1985
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Principal component analysis in linear systems: Controllability, observability, and model reduction
B.C. Moore · 1985
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Identification of observer Kalman filter Markov parameters: Theory and experiments
J. N. Juang, M. Phan, L. G. Horta, and R. W. Longman · 1991
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Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields
J. Guckenheimer and P. Holmes · 2002
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A subspace approach to balanced truncation for model reduction of nonlinear control systems
Sanjay Lall and Jerrold E. Marsden · 2002
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Balanced model reduction via the proper orthogonal decomposition
K. Willcox and J. Peraire · 2002
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Comparison of systems with complex behavior
Igor Mezić and Andrzej Banaszuk · 2004
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Model reduction for compressible flows using POD and Galerkin projection
C. W. Rowley, T. Colonius, and R. M. Murray · 2004
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Spectral properties of dynamical systems, model reduction and decompositions
I. Mezić · 2005
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Model reduction for fluids using balanced proper orthogonal decomposition
C.W. Rowley · 2005
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An overview of subspace identification
S. J. Qin · 2006
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Modeling of transitional channel flow using balanced proper orthogonal decomposition
M. Ilak and C.W. Rowley · 2008
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Dynamic mode decomposition of numerical and experimental data
P. J. Schmid and J. L. Sesterhenn · 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 and proper orthogonal decomposition of flow in a lid-driven cylindrical cavity
P. J. Schmid, K. E. Meyer, and O. Pust · 2009
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Dynamic mode decomposition of numerical and experimental data
P. J. Schmid · 2010
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Reduced order models for control of fluids using the eigensystem realization algorithm
Z. Ma, S. Ahuja, and C. W. Rowley · 2011
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Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data
P. Rapisarda and Trentelman H.L · 2011
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Application of the dynamic mode decomposition to experimental data
P. J. Schmid · 2011
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Applied koopmanism a)
Marko Budišić, Ryan Mohr, and Igor Mezić · 2012
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Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction
M. Grilli, P. J. Schmid, S. Hickel, and N. A. Adams · 2012
A kernel approach to data-driven koopman spectral analysis
Matthew O Williams, Clarence W Rowley, and Ioannis G Kevrekidis · 2014
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S. L. Brunton, B. W. Brunton, J. L. Proctor, and J. N. Kutz · 2015
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Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
S. L. Brunton, J.L.Proctor, and J. N. Kutz · 2015
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Compressive sampling dynamic mode decomposition
S. L. Brunton, J. L. Proctor, J. H. Tu, and J. N. Kutz · 2015
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Closed-loop turbulence control: Progress and challenges
S.L. Brunton and B.R. Noack · 2015
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Turbulence, coherent structures, dynamical systems and symmetry
P. J. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley · 2012
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Low-rank and sparse dynamic mode decomposition
M. R. Jovanović, P. J. Schmid, and J. W. Nichols · 2012
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Koopman-mode decomposition of the cylinder wake
S. Bagheri · 2013
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Dynamic mode decomposition for real-time background/foreground separation in video
J. Grosek and J. N. Kutz · 2013
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Analysis of fluid flows via spectral properties of the Koopman operator
I. Mezić · 2013
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Dimension reduction in a feedback loop using the SVD: Results on controllability and stability
R.C. Winck and W.J. Book · 2013
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Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
S. T. M. Dawson, M. S. Hemati, M. O. Williams, and C. W. Rowley · 2015
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A data-driven modeling framework for predicting forces and pressures on a rapidly pitching airfoil
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Data-driven model improvement for model-based control
M. Forgione, X. Bombois, and P.M.J Van den Hof · 2015
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A dynamic mode decomposition approach for large and arbitrarily sampled systems
F. Gueniat, L. Mathelin, and L. Pastur · 2015
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De-biasing the dynamic mode decomposition for applied koopman spectral analysis
Maziar S Hemati and Clarence W Rowley · 2015
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Discovering dynamic patterns from infectious disease data using dynamic mode decomposition
J.L. Proctor and P. A. Eckhoff · 2015
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A data-driven approximation of the koopman operator: extending dynamic mode decomposition
Matthew O Williams, Ioannis G Kevrekidis, and Clarence W Rowley · 2015
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Data fusion via intrinsic dynamic variables: An application of data-driven koopman spectral analysis
Matthew O Williams, Clarence W Rowley, Igor Mezić, and Ioannis G Kevrekidis · 2015
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Extracting spatial temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
Bingni W. Brunton, Lise A. Johnson, Jeffrey G. Ojemann, and J. Nathan Kutz · 2016
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Multi-resolution dynamic mode decomposition
J. N. Kutz, X. Fu, and S. L. Brunton · 2016
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Dynamic mode decomposition with control
J. L. Proctor, S. L. Brunton, and J. N. Kutz · 2016
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