%P 2228-2233
%T Sparse solutions to the average consensus problem via L1-Norm regularization of the fastest mixing Markov-Chain problem
%O 53rd Annual Conference on Decision and Control (CDC), held in Los Angeles (USA) 15-17 December 2014 
%I IEEE
%K Optimization, Sensor networks, Linear systems
%A Giorgio Gnecco
%A Rita Morisi
%A Alberto Bemporad
%X In the ?consensus problem? on multi-agent systems, in which the states of the agents are ?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 so as 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 regularized versions of the well-known fastest mixing Markov-chain problem, which are investigated theoretically. In particular, it is shown that such versions can be interpreted as ?robust? forms of the fastest mixing Markov-chain problem. Theoretical results useful to guide the choice of the regularization parameters are also provided, together with a numerical example.
%D 2014
%L eprints2480
%C Los Angeles (USA)
%B Proceedings of the 53rd Annual Conference on Decision and Control (CDC)
%R 10.1109/CDC.2014.7039729