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The Koopman framework proposes a linear representation of finite-dimensional nonlinear systems through a generally infinite-dimensional globally linear embedding.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
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Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics
A. Lasota and M. C. Mackey · 1994
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Nonlinear Control Systems
A. Isidori · 1995
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One-Parameter Semigroups for Linear Evolution Equations
K. J. Engel and R. Nagel · 2000
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Nonlinear systems; 3rd ed
H. K. Khalil · 2002
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Thomas’ Calculus, 11th Edition
G. T. Thomas, M. D. Weir, and F. Giordano J. R. Hass · 2005
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Modeling and Identification of Linear Parameter-Varying Systems
R. Tóth · 2010
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Control of Linear Parameter Varying Systems with Applications
J. Mohammadpour and C. W. Scherer · 2012
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Linear Parameter-Varying and Time-Delay Systems
C. Briat · 2016
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Linear identification of nonlinear systems: A lifting technique based on the Koopman operator
A. Mauroy and J. Goncalves · 2016
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Dynamic mode decomposition with control
J. L. Proctor, S. L. Brunton, and J. Nathan Kutz · 2016
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Koopman operator based observer synthesis for control-affine nonlinear systems
A. Surana · 2016
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Extending data-driven Koopman analysis to actuated systems
M. O. Williams, M. S. Hemati, S. T. M. Dawson, I. G. Kevrekidis, and C. W. Rowley · 2016
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Global bilinearization and controllability of control-affine nonlinear systems: A Koopman spectral approach
D. Goswami and D. A. Paley · 2017
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Feedback stabilization using Koopman operator
B. Huang, X. Ma, and U. Vaidya · 2018
Cited alongside, same era.
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
M. Korda and I. Mezić · 2018
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Decomposition of nonlinear dynamical systems using Koopman gramians
Z. Liu, S. Kundu, L. Chen, and E. Yeung · 2018
Cited alongside, same era.
Generalizing Koopman theory to allow for inputs and control
J. L. Proctor, S. L. Brunton, and J. Nathan Kutz · 2018
Derivative-based Koopman operators for real-time control of robotic systems
G. Mamakoukas, M. L. Castaño, X. Tan, and T. Murphey · 2020
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The Koopman Operator in Systems and Control: Concepts, Methodologies and Applications
A. Mauroy, I. Mezić, and Y. Susuki, editors · 2020
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Koopman operator dynamical models: Learning, analysis and control
P. Bevanda, S. Sosnowski, and S. Hirche · 2021
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Deep Koopman model predictive control for enhancing transient stability in power grids
Z. Ping, Z. Yin, X. Li, Y. Liu, and T. Yang · 2021
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Data-driven control of nonlinear systems: Learning Koopman operators for policy gradient
F. Zanini and A. Chiuso · 2021
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Modern Koopman theory for dynamical systems
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A Koopman operator approach for computing and balancing gramians for discrete time nonlinear systems
E. Yeung, Z. Liu, and N. O. Hodas · 2018
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Learning Koopman operators for systems with isolated critical points
C. Bakker, K. E. Nowak, and W. S. Rosenthal · 2019
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Estimating Koopman invariant subspaces of excited systems using artificial neural networks
M. Bonnert and U. Konigorski · 2020
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Data-driven approximations of dynamical systems operators for control
E. Kaiser, J. N. Kutz, and S. L. Brunton · 2020
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Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
S. Klus, F. Nüske, S. Peitz, J. H. Niemann, C. Clementi, and C. Schütte · 2020
Cited alongside, same era.
Optimal construction of Koopman eigenfunctions for prediction and control
M. Korda and I. Mezić · 2020
Cited alongside, same era.
S. L. Brunton, M. Budišić, E. Kaiser, and J. N. Kutz · 2022
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Optimal synthesis of LTI Koopman models for nonlinear systems with inputs
L. C. Iacob, R. Tóth, and M. Schoukens · 2022
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Identification of MIMO Wiener-type Koopman models for data-driven model reduction using deep learning
J. C. Schulze, D. T. Doncevic, and A. Mitsos · 2022
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Deep Koopman operator with control for nonlinear systems
H. Shi and M. Q.-H. Meng · 2022
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Finite dimensional Koopman form of polynomial nonlinear systems
L. C. Iacob, M. Schoukens, and R. Tóth · 2023
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Neural Koopman Lyapunov control
V. Zinage and E. Bakolas · 2023
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