Consensus on homogeneous manifolds

[en] The present paper considers distributed consensus algorithms for agents evolving on a connected compact homogeneous (CCH) manifold. The agents track no external reference and communicate their relative state according to an interconnection graph. The paper first formalizes the consensus problem for synchronization (i.e. maximizing the consensus) and balancing (i.e. minimizing the consensus); it thereby introduces the induced arithmetic mean, an easily computable mean position on CCH manifolds. Then it proposes and analyzes various consensus algorithms on manifolds: natural gradient algorithms which reach local consensus equilibria; an adaptation using auxiliary variables for almost-global synchronization or balancing; and a stochastic gossip setting for global synchronization. It closes by investigating the dependence of synchronization properties on the attraction function between interacting agents on the circle. The theory is also illustrated on SO(n) and on the Grassmann manifolds.

Research center :

Systems and Modeling

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Sarlette, Alain ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Sepulchre, Rodolphe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Language :

English

Title :

Consensus on homogeneous manifolds

Publication date :

December 2009

Event name :

48th IEEE Conference on Decision and Control

Event organizer :

IEEE

Event place :

Shanghai, China

Event date :

from 15-12-2009 to 18-12-2009

By request :

Yes

Audience :

International

Main work title :

Proceedings of the 48th IEEE Conference on Decision and Control

Pages :

6438-6443

Peer reviewed :

Peer reviewed

Additional URL :

http://www.montefiore.ulg.ac.be/~sarlette/publi.html

Funders :

This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office.

Commentary :

by request for presentation at the SIAM special session.

Available on ORBi :

since 10 February 2010

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Bibliography

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