Balance conditions in discrete-time consensus algorithms

Weiguo Xia; Guodong Shi; Ziyang Meng; Ming Cao; Karl Henrik Johansson

doi:10.1109/CDC.2017.8263753

Balance conditions in discrete-time consensus algorithms

Weiguo Xia^*, Guodong Shi, Ziyang Meng, Ming Cao, Karl Henrik Johansson

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

We study the consensus problem of discrete-time systems under persistent flow and non-reciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l₁ norm. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates are also provided in terms of the number of node interactions that have taken place.

Original language	English
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	769-774
Number of pages	6
ISBN (Electronic)	9781509028733
DOIs	https://doi.org/10.1109/CDC.2017.8263753
Publication status	Published - 28 Jun 2017
Event	56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia Duration: 12 Dec 2017 → 15 Dec 2017

Publication series

Name	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume	2018-January

Conference

Conference	56th IEEE Annual Conference on Decision and Control, CDC 2017
Country/Territory	Australia
City	Melbourne
Period	12/12/17 → 15/12/17

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10.1109/CDC.2017.8263753

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Xia, W., Shi, G., Meng, Z., Cao, M., & Johansson, K. H. (2017). Balance conditions in discrete-time consensus algorithms. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 769-774). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8263753

@inproceedings{09ef9d19892c44b29daaa4abb179166d,

title = "Balance conditions in discrete-time consensus algorithms",

abstract = "We study the consensus problem of discrete-time systems under persistent flow and non-reciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l1 norm. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates are also provided in terms of the number of node interactions that have taken place.",

author = "Weiguo Xia and Guodong Shi and Ziyang Meng and Ming Cao and Johansson, {Karl Henrik}",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.; 56th IEEE Annual Conference on Decision and Control, CDC 2017 ; Conference date: 12-12-2017 Through 15-12-2017",

year = "2017",

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doi = "10.1109/CDC.2017.8263753",

language = "English",

series = "2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017",

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Xia, W, Shi, G, Meng, Z, Cao, M & Johansson, KH 2017, Balance conditions in discrete-time consensus algorithms. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 769-774, 56th IEEE Annual Conference on Decision and Control, CDC 2017, Melbourne, Australia, 12/12/17. https://doi.org/10.1109/CDC.2017.8263753

Balance conditions in discrete-time consensus algorithms. / Xia, Weiguo; Shi, Guodong; Meng, Ziyang et al.
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 769-774 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January).

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

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AU - Shi, Guodong

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AU - Johansson, Karl Henrik

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Y1 - 2017/6/28

N2 - We study the consensus problem of discrete-time systems under persistent flow and non-reciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l1 norm. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates are also provided in terms of the number of node interactions that have taken place.

AB - We study the consensus problem of discrete-time systems under persistent flow and non-reciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l1 norm. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates are also provided in terms of the number of node interactions that have taken place.

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T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017

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ER -

Balance conditions in discrete-time consensus algorithms

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