Reference : Decentralised minimal-time consensus
Scientific congresses, symposiums and conference proceedings : Paper published in a book
Engineering, computing & technology : Multidisciplinary, general & others
Decentralised minimal-time consensus
Yuan, Y. mailto [> >]
Stan, G.-B. [> >]
Barahona, M. [> >]
Shi, L. [> >]
Goncalves, Jorge mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
The proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)
2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)
12-15 December 2011
Orlando, FL
[en] This study considers the discrete-time dynamics of a network of agents that exchange information according to the nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the consensus value of the whole network in finite time using only the minimal number of successive values of its own history. We show that this minimal number of steps is related to a Jordan block decomposition of the network dynamics and present an algorithm to obtain the minimal number of steps in question by checking a rank condition on a Hankel matrix of the local observations. Furthermore, we prove that the minimal number of steps is related to other algebraic and graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the underlying graph topology.

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