Fetching the paper…
Reading the bibliography…
We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs).
Hamiltonian Systems and Transformations in Hilbert Space
B. O. Koopman · 1931
Earlier work this paper cites.
Turbulence and the dynamics of coherent structures part I: coherent structures
L. Sirovich · 1987
Earlier work this paper cites.
Chaos, fractals, and noise: Stochastic aspects of dynamics
A. Lasota and M. C. Mackey · 1994
Earlier work this paper cites.
Limit occupational measures set for a control system and averaging of singularly perturbed control systems
V. Gaitsgory and A. Leizarowitz · 1999
Earlier work this paper cites.
Trust-region Methods for Flow Control based on Reduced Order Modelling
M. Fahl · 2000
Earlier work this paper cites.
Computational Methods for Fluid Dynamics
J. H. Ferziger and M. Peric · 2002
Earlier work this paper cites.
Receding horizon optimal control for infinite dimensional systems
K. Ito and K. Kunisch · 2002
Earlier work this paper cites.
Optimal Control of Switching Times in Switched Dynamical Systems
M. Egerstedt, Y. Wardi, and F. Delmotte · 2003
Earlier work this paper cites.
Switching in systems and control
D. Liberzon · 2003
Earlier work this paper cites.
Proper Orthogonal Decomposition Surrogate Models for Nonlinear Dynamical Systems: Error Estimates and Suboptimal Control
M. Hinze and S. Volkwein · 2005
Earlier work this paper cites.
The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows
B. R. Noack, P. Papas, and P. A. Monkewitz · 2005
Earlier work this paper cites.
Model Reduction for Fluids, Using Balanced Proper Orthogonal Decomposition
C. W. Rowley · 2005
Earlier work this paper cites.
OpenFOAM : A C++ Library for Complex Physics Simulations
H. Jasak, A. Jemcov, and Z. Tukovic · 2007
Earlier work this paper cites.
Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations
J. B. Lasserre, D. Henrion, C. Prieur, and E. Trélat · 2008
Cited alongside, same era.
Calibration of POD reduced-order models using Tikhonov regularization
L. Cordier, B. Abou El Majd, and J. Favier · 2009
Cited alongside, same era.
Spectral analysis of nonlinear flows
C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D. S. Henningson · 2009
Cited alongside, same era.
Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control
S. Sager · 2009
Cited alongside, same era.
POD a-posteriori error estimates for linear-quadratic optimal control problems
F. Tröltzsch and S. Volkwein · 2009
Cited alongside, same era.
Dynamic mode decomposition of numerical and experimental data
P. J. Schmid · 2010
Optimal Feedback Control of the Incompressible Navier-Stokes-Equations using Reduced Order Models
L. Pyta, M. Herty, and D. Abel · 2015
Later among the works it cites.
A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
M. O. Williams, I. G. Kevrekidis, and C. W. Rowley · 2015
Later among the works it cites.
Optimal control of hybrid switched systems: A brief survey
F. Zhu and P. J. Antsaklis · 2015
Later among the works it cites.
Modal occupation measures and LMI relaxations for nonlinear switched systems control
M. Claeys, J. Daafouz, and D. Henrion · 2016
Later among the works it cites.
On the numerical approximation of the Perron-Frobenius and Koopman operator
S. Klus, P. Koltai, and C. Schütte · 2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Nonlinear Stabilization via Control Lyapunov Measure
U. Vaidya, P. G. Mehta, and U. V. Shanbhag · 2010
Cited alongside, same era.
Applied Koopmanism
M. Budišić, R. Mohr, and I. Mezić · 2012
Cited alongside, same era.
The integer approximation error in mixed-integer optimal control
S. Sager, H. G. Bock, and M. Diehl · 2012
Cited alongside, same era.
Analysis of Fluid Flows via Spectral Properties of the Koopman Operator
I. Mezić · 2013
Cited alongside, same era.
Dynamic Mode Decomposition for Large and Streaming Datasets
M. S. Hemati, M. O. Williams, and C. W. Rowley · 2014
Cited alongside, same era.
On Dynamic Mode Decomposition: Theory and Applications
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz · 2014
Cited alongside, same era.
L. Grüne and J. Pannek · 2017
Closest in time.
Data-driven discovery of Koopman eigenfunctions for control
E. Kaiser, J. N. Kutz, and S. L. Brunton · 2017
Closest in time.
Second-Order Switching Time Optimization for Switched Dynamical Systems
B. Stellato, S. Ober-Blöbaum, and P. J. Goulart · 2017
Closest in time.
Tensor-based dynamic mode decomposition
S. Klus, P. Gelß, S. Peitz, and C. Schütte · 2018
Closest in time.
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
M. Korda and I. Mezić · 2018
Closest in time.
On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
M. Korda and I. Mezić · 2018
Closest in time.
Data-driven model reduction and transfer operator approximation
S. Klus, F. Nüske, P. Koltai, H. Wu, I. Kevrekidis, C. Schütte, and F. Noé · 2018
Closest in time.
Generalizing Koopman Theory to allow for inputs and control
J. L. Proctor, S. L. Brunton, and J. N. Kutz · 2018
Closest in time.