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Abstract: The present paper considers distributed consensus algorithms that involve Nagents evolving on a connected compact homogeneous manifold.
The agents trackno external reference and communicate their relative state according to acommunication graph.
The consensus problem is formulated in terms of theextrema of a cost function.
This leads to efficient gradient algorithms tosynchronize i.e.
maximizing the consensus or balance i.e.
minimizing theconsensus the agents; a convenient adaptation of the gradient algorithms isused when the communication graph is directed and time-varying.
The costfunction is linked to a specific centroid definition on manifolds, introducedhere as the induced arithmetic mean, that is easily computable in closed formand may be of independent interest for a number of manifolds.
The specialorthogonal group SOn and the Grassmann manifold Grp,n are treated asoriginal examples.
A link is also drawn with the many existing results on thecircle.

Autor: Alain Sarlette, Rodolphe Sepulchre



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