journal article Open Access Jul 01, 2018

Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control

Automatica Vol. 93 pp. 149-160 · Elsevier BV
View at Publisher Save 10.1016/j.automatica.2018.03.046
Topics

No keywords indexed for this article. Browse by subject →

References
26
[1]
Brunton "Chaos as an intermittently forced linear system" Nature communications (2017) 10.1038/s41467-017-00030-8
[2]
Brunton "Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control" PloS One (2016) 10.1371/journal.pone.0150171
[3]
Budišić "Applied koopmanism" Chaos. An Interdisciplinary Journal of Nonlinear Science (2012) 10.1063/1.4772195
[4]
Carleman "Application de la théorie des équations intégrales linéaires aux systémes d’équations différentielles non linéaires" Acta Mathematica (1932) 10.1007/bf02546499
[5]
Daniel-Berhe "Experimental physical parameter estimation of a thyristor driven DC-motor using the HMF-method" Control Engineering Practice (1998) 10.1016/s0967-0661(98)00036-7
[6]
Ferreau "qpOASES: A parametric active-set algorithm for quadratic programming" Mathematical Programming Computation (2014) 10.1007/s12532-014-0071-1
[7]
Grüne "Nonlinear model predictive control" (2011)
[8]
Klus "On the numerical approximation of the Perron-Frobenius and Koopman operator" Journal of Computational Dynamics (2016)
[9]
Hamiltonian Systems and Transformation in Hilbert Space

B. O. Koopman

Proceedings of the National Academy of Sciences 1931 10.1073/pnas.17.5.315
[10]
Koopman "Dynamical systems of continuous spectra" Proceedings of the National Academy of Sciences of the United States of America (1932) 10.1073/pnas.18.3.255
[11]
Korda Journal of Nonlinear Science (2018) 10.1007/s00332-017-9423-0
[12]
Ljung "System identification" (1998)
[13]
Mauroy, A., & Goncalves, J. (2016). Linear identification of nonlinear systems: A lifting technique based on the Koopman operator. In Conference on decision and control. 10.1109/cdc.2016.7799269
[14]
Mayne "Constrained model predictive control: Stability and optimality" Automatica (2000) 10.1016/s0005-1098(99)00214-9
[15]
Mezić "Spectral properties of dynamical systems, model reduction and decompositions" Nonlinear Dynamics (2005) 10.1007/s11071-005-2824-x
[16]
Mezić "Comparison of systems with complex behavior" Physica D (2004) 10.1016/j.physd.2004.06.015
[17]
Miura "The Korteweg–deVries equation: A survey of results" SIAM Review (1976) 10.1137/1018076
[18]
Proctor "Dynamic mode decomposition with control" SIAM Journal on Applied Dynamical Systems (2016) 10.1137/15m1013857
[19]
Proctor, J. L., Brunton, S. L., & Kutz, J. N. (2018). Generalizing Koopman theory to allow for inputs and control. SIAM Journal on Applied Dynamical Systems, in press. ArXiv preprint arXiv:1602.07647. 10.1137/16m1062296
[20]
Rawlings (2009)
[21]
Surana, A. (2016). Koopman operator based observer synthesis for control-affine nonlinear systems. In Conference on decision and control. 10.1109/cdc.2016.7799268
[22]
Surana, A., & Banaszuk, A. (2016). Linear observer synthesis for nonlinear systems using Koopman operator framework. In IFAC symposium on nonlinear control systems. 10.1016/j.ifacol.2016.10.250
[23]
On dynamic mode decomposition: Theory and applications

Jonathan H. Tu, Clarence W. Rowley, Dirk M. Luchtenburg et al.

Journal of Computational Dynamics 2014 10.3934/jcd.2014.1.391
[24]
Williams, M. O., Hemati, M. S., Dawson, S. T. M., Kevrekidis, I. G., & Rowley, C. W. (2016). Extending data-driven Koopman analysis to actuated systems. In IFAC symposium on nonlinear control systems (NOLCOS). 10.1016/j.ifacol.2016.10.248
[25]
Williams "A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition" Journal of Nonlinear Science (2015) 10.1007/s00332-015-9258-5
[26]
Williams "A kernel-based method for data-driven Koopman spectral analysis" Journal of Computational Dynamics (2015) 10.3934/jcd.2015005
Cited By
927
IEEE Robotics and Automation Letter...
Modern Koopman Theory for Dynamical Systems

Steven L. Brunton, Marko Budišić · 2022

SIAM Review
Nature Communications
Metrics
927
Citations
26
References
Details
Published
Jul 01, 2018
Vol/Issue
93
Pages
149-160
License
View
Funding
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung Award: P2ELP2_165166
Defense Advanced Research Projects Agency Award: HR0011-16-C-0116
Cite This Article
Milan Korda, IGOR MEZIĆ (2018). Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control. Automatica, 93, 149-160. https://doi.org/10.1016/j.automatica.2018.03.046
Related

You May Also Like

Constrained model predictive control: Stability and optimality

D.Q. Mayne, J.B. Rawlings · 2000

7,004 citations

Modeling by shortest data description

J. Rissanen · 1978

4,154 citations

Model predictive control: Theory and practice—A survey

Carlos E. García, David M. Prett · 1989

2,874 citations