The Observability Radius of Networks

Abstract : This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix and dedicated sensors are positioned at a subset of nodes. We allow for perturbations of certain edge weights with the objective of preventing observability of some modes of the network dynamics. To comply with the network setting, our work considers perturbations with a desired sparsity structure, thus extending the classic literature on the observability radius of linear systems. The paper proposes two sets of results. First, we propose an optimization framework to determine a perturbation with smallest Frobenius norm that renders a desired mode unobservable from the existing sensor nodes. Second, we study the expected observability radius of networks with given structure and random edge weights. We provide fundamental robustness bounds dependent on the connectivity properties of the network and we analytically characterize optimal perturbations of line and star networks, showing that line networks are inherently more robust than star networks.
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Article dans une revue
IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2017, 62 (6), pp.3006-3013. 〈10.1109/TAC.2016.2608941〉
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Contributeur : Paolo Frasca <>
Soumis le : samedi 27 mai 2017 - 22:13:45
Dernière modification le : vendredi 15 septembre 2017 - 13:16:50

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Gianluca Bianchin, Paolo Frasca, Andrea Gasparri, Fabio Pasqualetti. The Observability Radius of Networks. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2017, 62 (6), pp.3006-3013. 〈10.1109/TAC.2016.2608941〉. 〈hal-01528187〉

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