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Resistance-Based Performance Analysis of the Consensus Algorithm over Geometric Graphs

Lovisari, Enrico LU ; Garin, Federica and Zampieri, Sandro (2013) In SIAM Journal of Control and Optimization 51(5). p.3918-3945
Abstract
The performance of the linear consensus algorithm is studied by using a linear quadratic (LQ) cost. The objective is to understand how the communication topology influences this algorithm. This is achieved by exploiting the analogy between Markov chains and electrical resistive networks. Indeed, this allows us to uncover the relation between the LQ performance cost and the average effective resistance of a suitable electrical network and, moreover, to show that if the communication graph fulfills some local properties, then its behavior can be approximated by that of a grid, which is a graph whose associated LQ cost is well known.
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
multiagent systems, consensus algorithm, distributed averaging, large-scale graphs
in
SIAM Journal of Control and Optimization
volume
51
issue
5
pages
3918 - 3945
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • wos:000326384700023
  • scopus:84890470181
ISSN
1095-7138
DOI
10.1137/110857428
language
English
LU publication?
yes
id
db0f3473-0533-4822-9bcf-ddfdc056bdf3 (old id 4212507)
date added to LUP
2016-04-01 10:30:37
date last changed
2022-01-25 23:54:19
@article{db0f3473-0533-4822-9bcf-ddfdc056bdf3,
  abstract     = {{The performance of the linear consensus algorithm is studied by using a linear quadratic (LQ) cost. The objective is to understand how the communication topology influences this algorithm. This is achieved by exploiting the analogy between Markov chains and electrical resistive networks. Indeed, this allows us to uncover the relation between the LQ performance cost and the average effective resistance of a suitable electrical network and, moreover, to show that if the communication graph fulfills some local properties, then its behavior can be approximated by that of a grid, which is a graph whose associated LQ cost is well known.}},
  author       = {{Lovisari, Enrico and Garin, Federica and Zampieri, Sandro}},
  issn         = {{1095-7138}},
  keywords     = {{multiagent systems; consensus algorithm; distributed averaging; large-scale graphs}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{3918--3945}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal of Control and Optimization}},
  title        = {{Resistance-Based Performance Analysis of the Consensus Algorithm over Geometric Graphs}},
  url          = {{http://dx.doi.org/10.1137/110857428}},
  doi          = {{10.1137/110857428}},
  volume       = {{51}},
  year         = {{2013}},
}