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This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller.
Forced oscillations with variable natural frequency and their technical relevance
Georg Duffing · 1918
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Correlation and causation
Sewall Wright · 1921
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Hamiltonian systems and transformations in Hilbert space
Bernard O. Koopman · 1931
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Linear Robust Control
Michael Green and David J. N. Limebeer · 1994
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Numerical Methods for the Solution of Ill-Posed Problems
Andrey N. Tikhonov, Alexander Goncharsky, V. V. Stepanov, and Anatoly. G. Yagola · 1995
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Mahmoud Chilali, Pascal Gahinet, and Pierre Apkarian · 1999
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Tohru Katayama · 2005
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Sigurd Skogestad and Ian Postlethwaite · 2006
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Ali Rahimi and Benjamin Recht · 2007
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Applied Koopmanism
Marko Budišić, Ryan Mohr, and Igor Mezić · 2012
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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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Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems
Nathan J. Kutz, Steven L. Brunton, Bingni W. Brunton, and Joshua L. Proctor · 2016
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Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
Scott T. M. Dawson, Maziar S. Hemati, Matthew O. Williams, and Clarence W. Rowley · 2016
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Model-based control using Koopman operators
Ian Abraham, Gerardo de la Torre, and Todd Murphey · 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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On the structure of time-delay embedding in linear models of non-linear dynamical systems
Shaowu Pan and Karthik Duraisamy · 2020
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Data-driven discovery of Koopman eigenfunctions for control
Eurika Kaiser, J Nathan Kutz, and Steven L Brunton · 2021
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Koopman operators for estimation and control of dynamical systems
Samuel E. Otto and Clarence W. Rowley · 2021
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Data-driven Koopman controller synthesis based on the extended ℋ 2 \mathcal{H}_{2} norm characterization
Daisuke Uchida, Atsushi Yamashita, and Hajime Asama · 2021
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Advantages of bilinear Koopman realizations for the modeling and control of systems with unknown dynamics
Daniel Bruder, Xun Fu, and Ram Vasudevan · 2021
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Linear matrix inequality approaches to Koopman operator approximation
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Giuseppe Armenise, Marco Vaccari, Riccardo Bacci Di Capaci, and Gabriele Pannocchia · 2018
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Igor Mezić · 2019
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Active learning of dynamics for data-driven control using Koopman operators
Ian Abraham and Todd D. Murphey · 2019
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Lennart Ljung, Tianshi Chen, and Biqiang Mu · 2019
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Steven Dahdah and James Richard Forbes · 2021
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Koopman linearization for data-driven batch state estimation of control-affine systems
Zi Cong Guo, Vassili Korotkine, James R. Forbes, and Timothy D. Barfoot · 2022
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Modern Koopman theory for dynamical systems
Steven L. Brunton, Marko Budišić, Eurika Kaiser, and J. Nathan Kutz · 2022
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System norm regularization methods for Koopman operator approximation
Steven Dahdah and James R. Forbes · 2022
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Koopman-inspired approach for identification of exogenous anomalies in nonstationary time-series data
Alex Mallen, Christoph A Keller, and J Nathan Kutz · 2023
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