An asynchronous distributed algorithm for computing a common fixed point of a family of paracontractions

Daniel Fullmer; Ji Liu; A. Stephen Morse

doi:10.1109/CDC.2016.7798657

An asynchronous distributed algorithm for computing a common fixed point of a family of paracontractions

Daniel Fullmer
, Ji Liu
, A. Stephen Morse

Electrical Engineering

Stony Brook University

Yale University

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

16 Scopus citations

Abstract

A distributed algorithm is described for finding a common fixed point of a family of m > 1 nonlinear maps M_i : Rⁿ → Rⁿ assuming that each map is a paracontraction. The common fixed point is asynchronously computed in real time by m agents assuming each agent i knows only M_i, the current estimates of the fixed point generated by its neighbors, and nothing more. Each agent recursively updates its estimate of the fixed point at its own event times, by utilizing estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph N(t) whose vertices correspond to agents and whose arcs depict neighbor relations.

Original language	English
Title of host publication	2016 IEEE 55th Conference on Decision and Control, CDC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2620-2625
Number of pages	6
ISBN (Electronic)	9781509018376
DOIs	https://doi.org/10.1109/CDC.2016.7798657
State	Published - Dec 27 2016
Event	55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016

Publication series

Name	2016 IEEE 55th Conference on Decision and Control, CDC 2016

Conference

Conference	55th IEEE Conference on Decision and Control, CDC 2016
Country/Territory	United States
City	Las Vegas
Period	12/12/16 → 12/14/16

Access to Document

10.1109/CDC.2016.7798657

Cite this

Fullmer, D., Liu, J., & Stephen Morse, A. (2016). An asynchronous distributed algorithm for computing a common fixed point of a family of paracontractions. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 2620-2625). Article 7798657 (2016 IEEE 55th Conference on Decision and Control, CDC 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798657

@inproceedings{86d4a4ea1aa8448984bc5b4edfd12023,

title = "An asynchronous distributed algorithm for computing a common fixed point of a family of paracontractions",

abstract = "A distributed algorithm is described for finding a common fixed point of a family of m > 1 nonlinear maps Mi : Rn → Rn assuming that each map is a paracontraction. The common fixed point is asynchronously computed in real time by m agents assuming each agent i knows only Mi, the current estimates of the fixed point generated by its neighbors, and nothing more. Each agent recursively updates its estimate of the fixed point at its own event times, by utilizing estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph N(t) whose vertices correspond to agents and whose arcs depict neighbor relations.",

author = "Daniel Fullmer and Ji Liu and \{Stephen Morse\}, A.",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 55th IEEE Conference on Decision and Control, CDC 2016 ; Conference date: 12-12-2016 Through 14-12-2016",

year = "2016",

month = dec,

day = "27",

doi = "10.1109/CDC.2016.7798657",

language = "English",

series = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",

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

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booktitle = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",

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Fullmer, D, Liu, J & Stephen Morse, A 2016, An asynchronous distributed algorithm for computing a common fixed point of a family of paracontractions. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7798657, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers Inc., pp. 2620-2625, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7798657

An asynchronous distributed algorithm for computing a common fixed point of a family of paracontractions. / Fullmer, Daniel; Liu, Ji; Stephen Morse, A.
2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 2620-2625 7798657 (2016 IEEE 55th Conference on Decision and Control, CDC 2016).

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

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AU - Liu, Ji

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PY - 2016/12/27

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N2 - A distributed algorithm is described for finding a common fixed point of a family of m > 1 nonlinear maps Mi : Rn → Rn assuming that each map is a paracontraction. The common fixed point is asynchronously computed in real time by m agents assuming each agent i knows only Mi, the current estimates of the fixed point generated by its neighbors, and nothing more. Each agent recursively updates its estimate of the fixed point at its own event times, by utilizing estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph N(t) whose vertices correspond to agents and whose arcs depict neighbor relations.

AB - A distributed algorithm is described for finding a common fixed point of a family of m > 1 nonlinear maps Mi : Rn → Rn assuming that each map is a paracontraction. The common fixed point is asynchronously computed in real time by m agents assuming each agent i knows only Mi, the current estimates of the fixed point generated by its neighbors, and nothing more. Each agent recursively updates its estimate of the fixed point at its own event times, by utilizing estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph N(t) whose vertices correspond to agents and whose arcs depict neighbor relations.

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M3 - Conference contribution

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BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 55th IEEE Conference on Decision and Control, CDC 2016

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Fullmer D, Liu J, Stephen Morse A. An asynchronous distributed algorithm for computing a common fixed point of a family of paracontractions. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 2620-2625. 7798657. (2016 IEEE 55th Conference on Decision and Control, CDC 2016). doi: 10.1109/CDC.2016.7798657

An asynchronous distributed algorithm for computing a common fixed point of a family of paracontractions

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