The Smallest Eigenvalue of the Generalized Laplacian Matrix, with Application to Network-Decentralized Estimation for Homogeneous Systems
(2016) In IEEE Transactions on Network Science and Engineering 3(4). p.312-324- Abstract
- The problem of synthesizing network-decentralized observers arises when several agents, corresponding to the nodes of a network, exchange information about local measurements to asymptotically estimate their own state. The network topology is unknown to the nodes, which can rely on information about their neighboring nodes only. For homogeneous systems, composed of identical agents, we show that a network-decentralized observer can be designed by starting from local observers (typically, optimal filters) and then adapting the gain to ensure overall stability. The smallest eigenvalue of the so-called generalized Laplacian matrix is crucial: stability is guaranteed if the gain is greater than the inverse of this eigenvalue, which is strictly... (More)
- The problem of synthesizing network-decentralized observers arises when several agents, corresponding to the nodes of a network, exchange information about local measurements to asymptotically estimate their own state. The network topology is unknown to the nodes, which can rely on information about their neighboring nodes only. For homogeneous systems, composed of identical agents, we show that a network-decentralized observer can be designed by starting from local observers (typically, optimal filters) and then adapting the gain to ensure overall stability. The smallest eigenvalue of the so-called generalized Laplacian matrix is crucial: stability is guaranteed if the gain is greater than the inverse of this eigenvalue, which is strictly positive if the graph is externally connected. To deal with uncertain topologies, we characterize the worst-case smallest eigenvalue of the generalized Laplacian matrix for externally connected graphs, and we prove that the worst-case graph is a chain. This general result provides a bound for the observer gain that ensures robustness of the network-decentralized observer even under arbitrary, possibly switching, configurations, and in the presence of noise. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/e7247903-7020-43d5-a06e-dd1872637709
- author
- Giordano, Giulia LU ; Blanchini, F. ; Franco, Elisa ; Mardanlou, V. and Montessoro, P. L.
- organization
- publishing date
- 2016
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Eigenvalues and eigenfunctions, Laplace equations, Network topology, Observers, Robustness, Topology, Graph Theory, Network problems, generalized Laplacian matrix, network-decentralized estimation, network-decentralized observer
- in
- IEEE Transactions on Network Science and Engineering
- volume
- 3
- issue
- 4
- pages
- 312 - 324
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85012869448
- wos:000409674100010
- ISSN
- 2327-4697
- DOI
- 10.1109/TNSE.2016.2600026
- language
- English
- LU publication?
- yes
- id
- e7247903-7020-43d5-a06e-dd1872637709
- date added to LUP
- 2016-11-26 14:53:24
- date last changed
- 2024-05-03 14:40:17
@article{e7247903-7020-43d5-a06e-dd1872637709,
abstract = {{The problem of synthesizing network-decentralized observers arises when several agents, corresponding to the nodes of a network, exchange information about local measurements to asymptotically estimate their own state. The network topology is unknown to the nodes, which can rely on information about their neighboring nodes only. For homogeneous systems, composed of identical agents, we show that a network-decentralized observer can be designed by starting from local observers (typically, optimal filters) and then adapting the gain to ensure overall stability. The smallest eigenvalue of the so-called generalized Laplacian matrix is crucial: stability is guaranteed if the gain is greater than the inverse of this eigenvalue, which is strictly positive if the graph is externally connected. To deal with uncertain topologies, we characterize the worst-case smallest eigenvalue of the generalized Laplacian matrix for externally connected graphs, and we prove that the worst-case graph is a chain. This general result provides a bound for the observer gain that ensures robustness of the network-decentralized observer even under arbitrary, possibly switching, configurations, and in the presence of noise.}},
author = {{Giordano, Giulia and Blanchini, F. and Franco, Elisa and Mardanlou, V. and Montessoro, P. L.}},
issn = {{2327-4697}},
keywords = {{Eigenvalues and eigenfunctions; Laplace equations; Network topology; Observers; Robustness; Topology; Graph Theory; Network problems; generalized Laplacian matrix; network-decentralized estimation; network-decentralized observer}},
language = {{eng}},
number = {{4}},
pages = {{312--324}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Network Science and Engineering}},
title = {{The Smallest Eigenvalue of the Generalized Laplacian Matrix, with Application to Network-Decentralized Estimation for Homogeneous Systems}},
url = {{http://dx.doi.org/10.1109/TNSE.2016.2600026}},
doi = {{10.1109/TNSE.2016.2600026}},
volume = {{3}},
year = {{2016}},
}