Reference : Consensus optimization on manifolds
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
Consensus optimization on manifolds
Sarlette, Alain mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Sepulchre, Rodolphe mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
SIAM Journal on Control & Optimization
Society for Industrial & Applied Mathematics
Control and Optimization in Cooperative Networks
Yes (verified by ORBi)
[en] consensus algorithms ; decentralized control ; swarm control ; synchronization ; differential geometry ; mean on manifolds ; special orthogonal group ; Grassmann manifold
[en] 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.
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS

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