Agreement via the edge laplacian

Daniel Zelazo; Amirreza Rahmani; Mehran Mesbahi

doi:10.1109/CDC.2007.4434553

Agreement via the edge laplacian

Daniel Zelazo, Amirreza Rahmani, Mehran Mesbahi

Mechanical & Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

43 Scopus citations

Abstract

This work explores the properties of the edge variant of the graph Laplacian in the context of the edge agreement problem. We show that the edge Laplacian, and its corresponding agreement protocol, provide a useful perspective on the well-known node agreement, or the consensus problem. Specifically, the dynamics induced by the edge Laplacian facilitates a better understanding of the role played by certain subgraphs, e.g., cycles and spanning trees, in the original agreement problem. We also point out a reduced order modeling of the edge agreement as parameterized by the spanning trees of the underlying graph.

Original language	English (US)
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages	2309-2314
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2007.4434553
State	Published - Dec 1 2007
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	46th IEEE Conference on Decision and Control 2007, CDC
Country	United States
City	New Orleans, LA
Period	12/12/07 → 12/14/07

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2007.4434553

Cite this

Zelazo, D, Rahmani, A & Mesbahi, M 2007, Agreement via the edge laplacian. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434553, Proceedings of the IEEE Conference on Decision and Control, pp. 2309-2314, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434553

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author = "Daniel Zelazo and Amirreza Rahmani and Mehran Mesbahi",

year = "2007",

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doi = "10.1109/CDC.2007.4434553",

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series = "Proceedings of the IEEE Conference on Decision and Control",

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AB - This work explores the properties of the edge variant of the graph Laplacian in the context of the edge agreement problem. We show that the edge Laplacian, and its corresponding agreement protocol, provide a useful perspective on the well-known node agreement, or the consensus problem. Specifically, the dynamics induced by the edge Laplacian facilitates a better understanding of the role played by certain subgraphs, e.g., cycles and spanning trees, in the original agreement problem. We also point out a reduced order modeling of the edge agreement as parameterized by the spanning trees of the underlying graph.

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BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

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Agreement via the edge laplacian

Abstract

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