Built on

M. Budišić, R. Mohr, and I. Mezić, “Applied koopmanism,” Chaos: An Interdisciplinary Journal of Nonlinear Science
2012
Earlier work this paper cites.
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz, “On dynamic mode decomposition: Theory and applications,” Journal of Computational Dynamics
2014
Earlier work this paper cites.
M. O. Williams, C. W. Rowley, and I. G. Kevrekidis, “A kernel-based approach to data-driven koopman spectral analysis,” arXiv preprint arXiv:1411.2260
Original
2014
Earlier work this paper cites.
M. O. Williams, I. G. Kevrekidis, and C. W. Rowley, “A data–driven approximation of the koopman operator: Extending dynamic mode decomposition,” Journal of Nonlinear Science
2015
Earlier work this paper cites.
J. N. Kutz, J. L. Proctor, and S. L. Brunton, “Koopman theory for partial differential equations,” arXiv preprint arXiv:1607.07076
Original
2016
Earlier work this paper cites.

Similar

M. O. Williams, M. S. Hemati, S. T. Dawson, I. G. Kevrekidis, and C. W. Rowley, “Extending data-driven koopman analysis to actuated systems,” in IFAC Symposium on Nonlinear Control Systems (NOLCOS)
2016
Cited alongside, same era.
S. L. Brunton, B. W. Brunton, J. L. Proctor, and J. N. Kutz, “Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control,” PloS one
2016
Cited alongside, same era.
J. L. Proctor, S. L. Brunton, and J. N. Kutz, “Dynamic mode decomposition with control,” SIAM Journal on Applied Dynamical Systems
2016
Cited alongside, same era.
E. Yeung, S. Kundu, and N. Hodas, “Learning deep neural network representations for koopman operators of nonlinear dynamical systems,” arXiv preprint arXiv:1708.06850
Original
2017
Cited alongside, same era.

Then

E. Kaiser, J. N. Kutz, and S. L. Brunton, “Data-driven discovery of koopman eigenfunctions for control,” arXiv preprint arXiv:1707.01146
Original
2017
Later among the works it cites.
J. Page and R. R. Kerswell, “Koopman analysis of burgers equation,” Physical Review Fluids
2018
Later among the works it cites.
J. L. Proctor, S. L. Brunton, and J. N. Kutz, “Generalizing koopman theory to allow for inputs and control,” SIAM Journal on Applied Dynamical Systems
2018
Later among the works it cites.
M. Korda and I. Mezić, “Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control,” Automatica
2018
Later among the works it cites.
H. Arbabi, M. Korda, and I. Mezic, “A data-driven koopman model predictive control framework for nonlinear flows,” arXiv preprint arXiv:1804.05291
Original

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2019

Koopman Representations of Dynamic Systems with Control

Bakker, Craig, Rosenthal, Steven, Nowak, Kathleen E.

Understand

The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables.

Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow of the system onto a space of observables where the dynamics are linear (and possibly infinte).
This paper focuses on the development of consistent Koopman representations for controlled dynamical system.
We introduce the concept of dynamical consistency for Koopman representations and analyze several existing and proposed representations deriving necessary constraints on the dynamical system, observables, and Koopman operators.

Built on

M. Budišić, R. Mohr, and I. Mezić, “Applied koopmanism,” Chaos: An Interdisciplinary Journal of Nonlinear Science
2012
Earlier work this paper cites.
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz, “On dynamic mode decomposition: Theory and applications,” Journal of Computational Dynamics
2014
Earlier work this paper cites.
M. O. Williams, C. W. Rowley, and I. G. Kevrekidis, “A kernel-based approach to data-driven koopman spectral analysis,” arXiv preprint arXiv:1411.2260
Original
2014
Earlier work this paper cites.
M. O. Williams, I. G. Kevrekidis, and C. W. Rowley, “A data–driven approximation of the koopman operator: Extending dynamic mode decomposition,” Journal of Nonlinear Science
2015
Earlier work this paper cites.
J. N. Kutz, J. L. Proctor, and S. L. Brunton, “Koopman theory for partial differential equations,” arXiv preprint arXiv:1607.07076
Original
2016
Earlier work this paper cites.

Similar

M. O. Williams, M. S. Hemati, S. T. Dawson, I. G. Kevrekidis, and C. W. Rowley, “Extending data-driven koopman analysis to actuated systems,” in IFAC Symposium on Nonlinear Control Systems (NOLCOS)
2016
Cited alongside, same era.
S. L. Brunton, B. W. Brunton, J. L. Proctor, and J. N. Kutz, “Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control,” PloS one
2016
Cited alongside, same era.
J. L. Proctor, S. L. Brunton, and J. N. Kutz, “Dynamic mode decomposition with control,” SIAM Journal on Applied Dynamical Systems
2016
Cited alongside, same era.
E. Yeung, S. Kundu, and N. Hodas, “Learning deep neural network representations for koopman operators of nonlinear dynamical systems,” arXiv preprint arXiv:1708.06850
Original
2017
Cited alongside, same era.

Then

E. Kaiser, J. N. Kutz, and S. L. Brunton, “Data-driven discovery of koopman eigenfunctions for control,” arXiv preprint arXiv:1707.01146
Original
2017
Later among the works it cites.
J. Page and R. R. Kerswell, “Koopman analysis of burgers equation,” Physical Review Fluids
2018
Later among the works it cites.
J. L. Proctor, S. L. Brunton, and J. N. Kutz, “Generalizing koopman theory to allow for inputs and control,” SIAM Journal on Applied Dynamical Systems
2018
Later among the works it cites.
M. Korda and I. Mezić, “Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control,” Automatica
2018
Later among the works it cites.
H. Arbabi, M. Korda, and I. Mezic, “A data-driven koopman model predictive control framework for nonlinear flows,” arXiv preprint arXiv:1804.05291
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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Q. Li, F. Dietrich, E. M. Bollt, and I. G. Kevrekidis, “Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the koopman operator,” Chaos: An Interdisciplinary Journal of Nonlinear Science

2017

Cited alongside, same era.

2018

Later among the works it cites.