Linear identification of nonlinear systems: A lifting technique based on the Koopman operator

Alexandre Mauroy, Jorge Goncalves

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

Abstract

We exploit the key idea that nonlinear system identification is equivalent to linear identification of the so-called 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.

Original languageEnglish
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6500-6505
Number of pages6
ISBN (Electronic)9781509018376
DOIs
Publication statusPublished - 27 Dec 2016
Externally publishedYes
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: 12 Dec 201614 Dec 2016

Conference

Conference55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1614/12/16

Fingerprint

Nonlinear System Identification
Nonlinear systems
Identification (control systems)
Nonlinear Systems
Infinite-dimensional Spaces
State Space
Operator
Polynomial Vector Fields
Linear Least Squares
Network Dynamics
Chaotic systems
Open systems
Least Squares Problem
Decomposition Algorithm
Open Systems
Network Topology
Chaotic System
Vector Field
Unstable
Topology

Cite this

Mauroy, A., & Goncalves, J. (2016). Linear identification of nonlinear systems: A lifting technique based on the Koopman operator. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 6500-6505). [7799269] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7799269
Mauroy, Alexandre ; Goncalves, Jorge. / Linear identification of nonlinear systems : A lifting technique based on the Koopman operator. 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 6500-6505
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Mauroy, A & Goncalves, J 2016, Linear identification of nonlinear systems: A lifting technique based on the Koopman operator. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7799269, Institute of Electrical and Electronics Engineers Inc., pp. 6500-6505, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7799269

Linear identification of nonlinear systems : A lifting technique based on the Koopman operator. / Mauroy, Alexandre; Goncalves, Jorge.

2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 6500-6505 7799269.

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

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Mauroy A, Goncalves J. Linear identification of nonlinear systems: A lifting technique based on the Koopman operator. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 6500-6505. 7799269 https://doi.org/10.1109/CDC.2016.7799269