On asymptotic properties of continuous-time stochastic approximation type consensus protocols

Huaibin Tang; Tao Li

doi:10.1109/CDC.2014.7039726

On asymptotic properties of continuous-time stochastic approximation type consensus protocols

Huaibin Tang
, Tao Li

Shandong University
Shanghai University

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

4 Scopus citations

Abstract

For the multi-agent consensus with stochastic communication noises, the stochastic approximation type protocol is an effective method. In this paper, we will analyze the asymptotic properties of continuous-time stochastic approximation type consensus protocols in both mean square and probability one. We clarify the relationship between the convergence rate of the consensus error and a representative class of consensus gains. Different from the previous literature in which stochastic Lyapunov functions and the supermartingale convergence theorem were used, basic results of stochastic analysis and algebraic graph theory are used in this paper. By the law of the iterated logarithm of stochastic integrals, more precise estimates of the convergence rate are given.

Original language	English
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2210-2215
Number of pages	6
Edition	February
ISBN (Electronic)	9781479977468
DOIs	https://doi.org/10.1109/CDC.2014.7039726
State	Published - 2014
Externally published	Yes
Event	53rd IEEE Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: 15 Dec 2014 → 17 Dec 2014

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2014-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	53rd IEEE Conference on Decision and Control, CDC 2014
Country/Territory	United States
City	Los Angeles
Period	15/12/14 → 17/12/14

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10.1109/CDC.2014.7039726

Cite this

Tang, H., & Li, T. (2014). On asymptotic properties of continuous-time stochastic approximation type consensus protocols. In 53rd IEEE Conference on Decision and Control,CDC 2014 (February ed., pp. 2210-2215). Article 7039726 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2014-December, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7039726

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title = "On asymptotic properties of continuous-time stochastic approximation type consensus protocols",

abstract = "For the multi-agent consensus with stochastic communication noises, the stochastic approximation type protocol is an effective method. In this paper, we will analyze the asymptotic properties of continuous-time stochastic approximation type consensus protocols in both mean square and probability one. We clarify the relationship between the convergence rate of the consensus error and a representative class of consensus gains. Different from the previous literature in which stochastic Lyapunov functions and the supermartingale convergence theorem were used, basic results of stochastic analysis and algebraic graph theory are used in this paper. By the law of the iterated logarithm of stochastic integrals, more precise estimates of the convergence rate are given.",

author = "Huaibin Tang and Tao Li",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 53rd IEEE Conference on Decision and Control, CDC 2014 ; Conference date: 15-12-2014 Through 17-12-2014",

year = "2014",

doi = "10.1109/CDC.2014.7039726",

language = "英语",

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

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Tang, H & Li, T 2014, On asymptotic properties of continuous-time stochastic approximation type consensus protocols. in 53rd IEEE Conference on Decision and Control,CDC 2014. February edn, 7039726, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2014-December, Institute of Electrical and Electronics Engineers Inc., pp. 2210-2215, 53rd IEEE Conference on Decision and Control, CDC 2014, Los Angeles, United States, 15/12/14. https://doi.org/10.1109/CDC.2014.7039726

On asymptotic properties of continuous-time stochastic approximation type consensus protocols. / Tang, Huaibin; Li, Tao.
53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. p. 2210-2215 7039726 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2014-December, No. February).

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

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N2 - For the multi-agent consensus with stochastic communication noises, the stochastic approximation type protocol is an effective method. In this paper, we will analyze the asymptotic properties of continuous-time stochastic approximation type consensus protocols in both mean square and probability one. We clarify the relationship between the convergence rate of the consensus error and a representative class of consensus gains. Different from the previous literature in which stochastic Lyapunov functions and the supermartingale convergence theorem were used, basic results of stochastic analysis and algebraic graph theory are used in this paper. By the law of the iterated logarithm of stochastic integrals, more precise estimates of the convergence rate are given.

AB - For the multi-agent consensus with stochastic communication noises, the stochastic approximation type protocol is an effective method. In this paper, we will analyze the asymptotic properties of continuous-time stochastic approximation type consensus protocols in both mean square and probability one. We clarify the relationship between the convergence rate of the consensus error and a representative class of consensus gains. Different from the previous literature in which stochastic Lyapunov functions and the supermartingale convergence theorem were used, basic results of stochastic analysis and algebraic graph theory are used in this paper. By the law of the iterated logarithm of stochastic integrals, more precise estimates of the convergence rate are given.

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ER -

On asymptotic properties of continuous-time stochastic approximation type consensus protocols

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