### 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 language | English |
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Title of host publication | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 6500-6505 |

Number of pages | 6 |

ISBN (Electronic) | 9781509018376 |

DOIs | |

Publication status | Published - 27 Dec 2016 |

Externally published | Yes |

Event | 55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: 12 Dec 2016 → 14 Dec 2016 |

### Conference

Conference | 55th IEEE Conference on Decision and Control, CDC 2016 |
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Country | United States |

City | Las Vegas |

Period | 12/12/16 → 14/12/16 |

### Fingerprint

### Cite this

*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

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*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.

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Linear identification of nonlinear systems

T2 - A lifting technique based on the Koopman operator

AU - Mauroy, Alexandre

AU - Goncalves, Jorge

PY - 2016/12/27

Y1 - 2016/12/27

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85010715555&partnerID=8YFLogxK

U2 - 10.1109/CDC.2016.7799269

DO - 10.1109/CDC.2016.7799269

M3 - Conference contribution

AN - SCOPUS:85010715555

SP - 6500

EP - 6505

BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -