Localized high-order consensus destabilizes large-scale networks
(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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- author
- Tegling, Emma LU ; Bamieh, Bassam and Sandberg, Henrik LU
- publishing date
- 2019-07
- 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}}, }