CUED Publications database

Consensus optimization on manifolds

Sarlette, A and Sepulchre, R (2009) Consensus optimization on manifolds. SIAM Journal on Control and Optimization, 48. pp. 56-76. ISSN 0363-0129

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Abstract

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO (n) and the Grassmann manifold Grass (p, n) are treated as original examples. A link is also drawn with the many existing results on the circle. © 2009 Society for Industrial and Applied Mathematics.

Item Type: Article
Uncontrolled Keywords: Consensus algorithms Decentralized control Differential geometry Grassmann manifold Mean on manifolds Special orthogonal group Swarm control Synchronization
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:25
Last Modified: 08 Dec 2014 02:18
DOI: 10.1137/060671425