4 research outputs found
The Projection Method for Reaching Consensus and the Regularized Power Limit of a Stochastic Matrix
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 Comment: 19 pages, 2 figure