Persistent graphs and consensus convergence
2012 (English)In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE conference proceedings, 2012, 2046-2051 p.Conference paper (Refereed)
This paper investigates the role persistent arcs play for averaging algorithms to reach a global consensus under discrete-time or continuous-time dynamics. Each (directed) arc in the underlying communication graph is assumed to be associated with a time-dependent weight function. An arc is said to be persistent if its weight function has infinite ℒ1 or ℓ1 norm for continuous-time or discrete-time models, respectively. The graph that consists of all persistent arcs is called the persistent graph of the underlying network. Three necessary and sufficient conditions on agreement or ε-agreement are established, by which we prove that the persistent graph fully determines the convergence to a consensus. It is also shown how the convergence rates explicitly depend on the diameter of the persistent graph.
Place, publisher, year, edition, pages
IEEE conference proceedings, 2012. 2046-2051 p.
, IEEE Conference on Decision and Control. Proceedings, ISSN 0191-2216
Averaging Algorithms, Consensus, Persistent Graphs
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-111454DOI: 10.1109/CDC.2012.6426728ISI: 000327200402070ScopusID: 2-s2.0-84874267009ISBN: 978-1-4673-2064-1OAI: oai:DiVA.org:kth-111454DiVA: diva2:586421
51st IEEE Conference on Decision and Control, CDC 2012; Maui, HI; United States; 10 December 2012 through 13 December 2012
Qc 201302122013-02-122013-01-112013-12-20Bibliographically approved