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Linear identification of nonlinear systems: A lifting technique based on the Koopman operator
Mauroy, Alexandre; Goncalves, Jorge
2016In Proceedings of the 55th IEEE Conference on Decision and Control
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Keywords :
system identification; network inference; Koopman operator
Abstract :
[en] We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification technique by recasting the problem in the infinite-dimensional space of observables. This technique can be described in two main steps. In the first step, similar to a component of the Extended Dynamic Mode Decomposition algorithm, the data are lifted to the infinite-dimensional space and used for linear identification of the Koopman operator. In the second step, the obtained Koopman operator is “projected back” to the finite-dimensional state space, and identified to the nonlinear vector field through a linear least squares problem. The proposed technique is efficient to recover (polynomial) vector fields of different classes of systems, including unstable, chaotic, and open systems. In addition, it is robust to noise, well-suited to model low sampling rate datasets, and able to infer network topology and dynamics.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Mathematics
Author, co-author :
Mauroy, Alexandre ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Goncalves, Jorge ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
External co-authors :
no
Language :
English
Title :
Linear identification of nonlinear systems: A lifting technique based on the Koopman operator
Publication date :
December 2016
Event name :
55th IEEE Conference on Decision and Control
Event organizer :
IEEE
Event place :
Las Vegas, United States
Event date :
from 12-12-2016 to 14-12-2016
Audience :
International
Main work title :
Proceedings of the 55th IEEE Conference on Decision and Control
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 27 August 2016

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