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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.

Author: Alain Sarlette, Rodolphe Sepulchre


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