Paper Info
Title
Theorems about ergodicity and class-ergodicity of chains with applications in known consensus models.
Abstract
In a multi-agent system, unconditional (multiple) consensus is the property of reaching to (multiple) consensus irrespective of the instant and values at which states are initialized. For linear algorithms, occurrence of unconditional (multiple) consensus turns out to be equivalent to (class-) ergodicity of the transition chain (A_n). For a wide class of chains, chains with so-called balanced asymmetry property, necessary and sufficient conditions for ergodicity and class-ergodicity are derived. The results are employed to analyze the limiting behavior of agents' states in the JLM model, the Krause model, and the Cucker-Smale model. In particular, unconditional single or multiple consensus occurs in all three models. Moreover, a necessary and sufficient condition for unconditional consensus in the JLM model and a sufficient condition for consensus in the Cucker-Smale model are obtained.
Year
DOI
Venue
2012
10.1109/Allerton.2012.6483385
Allerton Conference
Keywords
Field
DocType
multi-agent systems,Cucker-Smale model,JLM model,Krause model,class ergodicity,consensus models,linear algorithms,multiagent system,transition chain,Cucker-Smale model,JLM model,Unconditional single or multiple consensus,ergodicity or class-ergodicity,multi-agent systems
Discrete mathematics,Topology,Applied mathematics,Ergodicity,Asymmetry,Limiting,Mathematics
Conference
ISSN
Citations 
PageRank 
2474-0195
2
0.38
References 
Authors
0
2
Name
Order
Citations
PageRank
Sadegh Bolouki1186.92
Roland P. Malhamé222031.40