Abstract
In the coordination problems 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. Let P be a row stochastic influence matrix, whereas TP is the subspace of initial opinions that ensure consensus in DeGroot's iterative pooling model. We propose a method of coordination that consists of: (1) transformation of the vector of initial opinions into the closest vector in TP and (2) subsequent DeGroot process with the matrix P.
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