Sarlette, A and Sepulchre, R (2009) Consensus optimization on manifolds. SIAM Journal on Control and Optimization, 48. pp. 56-76. ISSN 0363-0129Full text not available from this repository.
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.
|Uncontrolled Keywords:||Consensus algorithms Decentralized control Differential geometry Grassmann manifold Mean on manifolds Special orthogonal group Swarm control Synchronization|
|Divisions:||Div F > Control|
|Depositing User:||Cron Job|
|Date Deposited:||07 Mar 2014 11:25|
|Last Modified:||08 Dec 2014 02:18|