Linear identification of nonlinear systems: A lifting technique based on the Koopman operator
作者： Alexandre Mauroy , Jorge Goncalves
关键词: Nonlinear system 、 Observable 、 System identification 、 Operator (physics) 、 State space 、 Dynamic mode decomposition 、 Algorithm 、 Nonlinear system identification 、 Mathematics 、 Linear least squares 、 Control theory
摘要: … While Koopman operator techniques have been previously considered in the framework of … obtained through the Koopman operator, our key idea is to identify a linear operator in the …
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Andrzej Lasota, Michael C. Mackey, Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics ,(1993)
Matthew O. Williams, Ioannis G. Kevrekidis, Clarence W. Rowley, A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition Journal of Nonlinear Science. ,vol. 25, pp. 1307- 1346 ,(2015) , 10.1007/S00332-015-9258-5
PETER J. SCHMID, Dynamic mode decomposition of numerical and experimental data Journal of Fluid Mechanics. ,vol. 656, pp. 5- 28 ,(2010) , 10.1017/S0022112010001217
Wei Pan, Ye Yuan, Jorge Goncalves, Guy-Bart Stan, A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems IEEE Transactions on Automatic Control. ,vol. 61, pp. 182- 187 ,(2016) , 10.1109/TAC.2015.2426291
Igor Mezić, Spectral Properties of Dynamical Systems, Model Reduction and Decompositions Nonlinear Dynamics. ,vol. 41, pp. 309- 325 ,(2005) , 10.1007/S11071-005-2824-X
Yueheng Lan, Igor Mezić, Linearization in the large of nonlinear systems and Koopman operator spectrum Physica D: Nonlinear Phenomena. ,vol. 242, pp. 42- 53 ,(2013) , 10.1016/J.PHYSD.2012.08.017
Robert Tibshirani, Regression Shrinkage and Selection Via the Lasso Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 58, pp. 267- 288 ,(1996) , 10.1111/J.2517-6161.1996.TB02080.X
CLARENCE W. ROWLEY, IGOR MEZIĆ, SHERVIN BAGHERI, PHILIPP SCHLATTER, DAN S. HENNINGSON, Spectral analysis of nonlinear flows Journal of Fluid Mechanics. ,vol. 641, pp. 115- 127 ,(2009) , 10.1017/S0022112009992059
Alexandre Mauroy, Aivar Sootla, Operator-Theoretic Characterization of Eventually Monotone Systems arXiv: Dynamical Systems. ,(2015)
Steven L. Brunton, Joshua L. Proctor, J. Nathan Kutz, Discovering governing equations from data by sparse identification of nonlinear dynamical systems Proceedings of the National Academy of Sciences of the United States of America. ,vol. 113, pp. 3932- 3937 ,(2016) , 10.1073/PNAS.1517384113