Spectral identification of networks with inputs

Alexandre Mauroy, J.M. Hendrickx

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

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Abstract

We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These eigenvalues allow to deduce some global properties of the network, such as bounds on the node degree. Having recently introduced this approach for autonomous networks of nonlinear systems, we extend it here to treat networked systems with external inputs on the nodes, in the case of linear dynamics. This is more natural in several applications, and removes the need to sometimes use several independent trajectories. We illustrate our framework with several examples, where we estimate the mean, minimum, and maximum node degree in the network. Inferring some information on the leading Laplacian eigenvectors, we also use our framework in the context of network clustering.
Original languageEnglish
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages469–474
Number of pages6
Volume2018-January
ISBN (Electronic)9781509028733
ISBN (Print)9781509028733
DOIs
Publication statusPublished - 18 Jan 2018
Event56th IEEE Conference on Decision and Control - Melbourne, Australia
Duration: 12 Dec 201715 Dec 2017
Conference number: 56

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Conference

Conference56th IEEE Conference on Decision and Control
CountryAustralia
CityMelbourne
Period12/12/1715/12/17

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Eigenvalues and eigenfunctions
Nonlinear systems
Dynamical systems
Trajectories

Cite this

Mauroy, A., & Hendrickx, J. M. (2018). Spectral identification of networks with inputs. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (Vol. 2018-January, pp. 469–474). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8263708
Mauroy, Alexandre ; Hendrickx, J.M. / Spectral identification of networks with inputs. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Vol. 2018-January Institute of Electrical and Electronics Engineers Inc., 2018. pp. 469–474 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017).
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title = "Spectral identification of networks with inputs",
abstract = "We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These eigenvalues allow to deduce some global properties of the network, such as bounds on the node degree. Having recently introduced this approach for autonomous networks of nonlinear systems, we extend it here to treat networked systems with external inputs on the nodes, in the case of linear dynamics. This is more natural in several applications, and removes the need to sometimes use several independent trajectories. We illustrate our framework with several examples, where we estimate the mean, minimum, and maximum node degree in the network. Inferring some information on the leading Laplacian eigenvectors, we also use our framework in the context of network clustering.",
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Mauroy, A & Hendrickx, JM 2018, Spectral identification of networks with inputs. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. vol. 2018-January, 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 469–474, 56th IEEE Conference on Decision and Control, Melbourne, Australia, 12/12/17. https://doi.org/10.1109/CDC.2017.8263708

Spectral identification of networks with inputs. / Mauroy, Alexandre; Hendrickx, J.M.

2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Vol. 2018-January Institute of Electrical and Electronics Engineers Inc., 2018. p. 469–474 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January).

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

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N2 - We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These eigenvalues allow to deduce some global properties of the network, such as bounds on the node degree. Having recently introduced this approach for autonomous networks of nonlinear systems, we extend it here to treat networked systems with external inputs on the nodes, in the case of linear dynamics. This is more natural in several applications, and removes the need to sometimes use several independent trajectories. We illustrate our framework with several examples, where we estimate the mean, minimum, and maximum node degree in the network. Inferring some information on the leading Laplacian eigenvectors, we also use our framework in the context of network clustering.

AB - We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These eigenvalues allow to deduce some global properties of the network, such as bounds on the node degree. Having recently introduced this approach for autonomous networks of nonlinear systems, we extend it here to treat networked systems with external inputs on the nodes, in the case of linear dynamics. This is more natural in several applications, and removes the need to sometimes use several independent trajectories. We illustrate our framework with several examples, where we estimate the mean, minimum, and maximum node degree in the network. Inferring some information on the leading Laplacian eigenvectors, we also use our framework in the context of network clustering.

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Mauroy A, Hendrickx JM. Spectral identification of networks with inputs. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Vol. 2018-January. Institute of Electrical and Electronics Engineers Inc. 2018. p. 469–474. (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017). https://doi.org/10.1109/CDC.2017.8263708