The Projection Method for Reaching Consensus and the Regularized Power Limit of a Stochastic Matrix
Abstract
In the coordination/consensus problem for multi-agent systems, a well-known condition of achieving consensus is the presence of a spanning arborescence in the communication digraph. The paper deals with the discrete consensus problem in the case where this condition is not satisfied. A characterization of the subspace of initial opinions (where is the influence matrix) that \emph{ensure} consensus in the DeGroot model is given. We propose a method of coordination that consists of: (1) the transformation of the vector of initial opinions into a vector belonging to by orthogonal projection and (2) subsequent iterations of the transformation The properties of this method are studied. It is shown that for any non-periodic stochastic matrix the resulting matrix of the orthogonal projection method can be treated as a regularized power limit of
Keywords
Cite
@article{arxiv.1109.3948,
title = {The Projection Method for Reaching Consensus and the Regularized Power Limit of a Stochastic Matrix},
author = {R. P. Agaev and P. Yu. Chebotarev},
journal= {arXiv preprint arXiv:1109.3948},
year = {2012}
}
Comments
19 pages, 2 figures