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Localized high-order consensus destabilizes large-scale networks

Tegling, Emma LU ; Bamieh, Bassam and Sandberg, Henrik LU (2019) 2019 American Control Conference, ACC 2019 In Proceedings of the American Control Conference 2019-July. p.760-765
Abstract

We study the problem of distributed consensus in networks where the local agents have high-order (n ≥ 3) integrator dynamics, and where all feedback is localized in that each agent has a bounded number of neighbors. We prove that no consensus algorithm based on relative differences between states of neighboring agents can then achieve consensus in networks of any size. That is, while a given algorithm may allow a small network to converge to consensus, the same algorithm will lead to instability if agents are added to the network so that it grows beyond a certain finite size. This holds in classes of network graphs whose algebraic connectivity, that is, the smallest non-zero Laplacian eigenvalue, is decreasing towards zero in network... (More)

We study the problem of distributed consensus in networks where the local agents have high-order (n ≥ 3) integrator dynamics, and where all feedback is localized in that each agent has a bounded number of neighbors. We prove that no consensus algorithm based on relative differences between states of neighboring agents can then achieve consensus in networks of any size. That is, while a given algorithm may allow a small network to converge to consensus, the same algorithm will lead to instability if agents are added to the network so that it grows beyond a certain finite size. This holds in classes of network graphs whose algebraic connectivity, that is, the smallest non-zero Laplacian eigenvalue, is decreasing towards zero in network size. This applies, for example, to all planar graphs. Our proof, which relies on Routh-Hurwitz criteria for complex-valued polynomials, holds true for directed graphs with normal graph Laplacians. We survey classes of graphs where this issue arises, and also discuss leader-follower consensus, where instability will arise in any growing, undirected network as long as the feedback is localized.

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Please use this url to cite or link to this publication:
author
; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2019 American Control Conference, ACC 2019
series title
Proceedings of the American Control Conference
volume
2019-July
article number
8815369
pages
6 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
2019 American Control Conference, ACC 2019
conference location
Philadelphia, United States
conference dates
2019-07-10 - 2019-07-12
external identifiers
  • scopus:85072275786
ISSN
0743-1619
ISBN
9781538679265
DOI
10.23919/acc.2019.8815369
project
Fundamental mechanisms for scalable control of large networks
language
English
LU publication?
no
additional info
Publisher Copyright: © 2019 American Automatic Control Council.
id
68703ebb-e6ca-425b-b8e2-eb3da1cf7adb
date added to LUP
2021-11-24 09:50:22
date last changed
2023-01-24 21:11:42
@inproceedings{68703ebb-e6ca-425b-b8e2-eb3da1cf7adb,
  abstract     = {{<p>We study the problem of distributed consensus in networks where the local agents have high-order (n ≥ 3) integrator dynamics, and where all feedback is localized in that each agent has a bounded number of neighbors. We prove that no consensus algorithm based on relative differences between states of neighboring agents can then achieve consensus in networks of any size. That is, while a given algorithm may allow a small network to converge to consensus, the same algorithm will lead to instability if agents are added to the network so that it grows beyond a certain finite size. This holds in classes of network graphs whose algebraic connectivity, that is, the smallest non-zero Laplacian eigenvalue, is decreasing towards zero in network size. This applies, for example, to all planar graphs. Our proof, which relies on Routh-Hurwitz criteria for complex-valued polynomials, holds true for directed graphs with normal graph Laplacians. We survey classes of graphs where this issue arises, and also discuss leader-follower consensus, where instability will arise in any growing, undirected network as long as the feedback is localized.</p>}},
  author       = {{Tegling, Emma and Bamieh, Bassam and Sandberg, Henrik}},
  booktitle    = {{2019 American Control Conference, ACC 2019}},
  isbn         = {{9781538679265}},
  issn         = {{0743-1619}},
  language     = {{eng}},
  pages        = {{760--765}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{Proceedings of the American Control Conference}},
  title        = {{Localized high-order consensus destabilizes large-scale networks}},
  url          = {{http://dx.doi.org/10.23919/acc.2019.8815369}},
  doi          = {{10.23919/acc.2019.8815369}},
  volume       = {{2019-July}},
  year         = {{2019}},
}