%0 Journal Article
%@ 2327-4697
%A Gnecco, Giorgio
%A Morisi, Rita
%A Bemporad, Alberto
%D 2015
%F eprints:2774
%I IEEE
%J IEEE Transactions on Network Science and Engineering
%K Artificial neural networks; Convergence; Convex functions; Eigenvalues and eigenfunctions; Optimization; Symmetric matrices; Wireless sensor networks; Consensus; Fastest Mixing Markov-Chain problem; Optimization; Regularization; Sparsity
%N 3
%P 97-111
%T Sparse Solutions to the Average Consensus Problem via Various Regularizations of the Fastest Mixing Markov-Chain Problem
%U http://eprints.imtlucca.it/2774/
%V 2
%X In the consensus problem on multi-agent systems, in which the states of the agents represent opinions, the agents aim at reaching a common opinion (or consensus state) through local exchange of information. An important design problem is to choose the degree of interconnection of the subsystems to achieve a good trade-off between a small number of interconnections and a fast convergence to the consensus state, which is the average of the initial opinions under mild conditions. This paper addresses this problem through l₁ -norm and l₀ -“pseudo-norm” regularized versions of the well-known Fastest Mixing Markov-Chain (FMMC) problem. We show that such versions can be interpreted as robust forms of the FMMC problem and provide results to guide the choice of the regularization parameter.