Reference : Global synchronization on the circle
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Global synchronization on the circle
Sarlette, Alain mailto [Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Tuna, Sezai Emre mailto [Université de Liège - ULiège > Dpt. Electricité, électronique et informatique (Institut Montefiore) > Systems & Modeling > >]
Blondel, Vincent mailto [Université Catholique de Louvain - UCL > Mathematical Engineering > Large graphs and networks > >]
Sepulchre, Rodolphe mailto [Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Proceedings of the 17th IFAC World Congress
17th IFAC World Congress
[en] consensus on circle ; multi-agent system ; time-variant communication topology ; gossip algorithm
[en] The convexity arguments used in the consensus literature to prove synchronization in vector spaces can be applied to the circle only when all agents are initially located on a semicircle. Existing strategies for (almost-)global synchronization on the circle are either restricted to specific interconnection topologies or use auxiliary variables. The present paper first illustrates this problem by showing that weighted, directed interconnection topologies can be designed to make any reasonably chosen configuration of the agents on the circle a stable equilibrium of a basic continuous-time consensus algorithm. Then it proposes a so-called “gossip algorithm”, which achieves global asymptotic synchronization on the circle with probability 1 for a large class of interconnections, without using auxiliary variables, thanks to the introduction of randomness in the system.

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