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

## 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 |
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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: | 04 Feb 2015 22:05 |

Last Modified: | 16 Feb 2015 01:18 |

DOI: | 10.1137/060671425 |