%0 Book Section
%A Gnecco, Giorgio
%A Morisi, Rita
%A Bemporad, Alberto
%B Proceedings of the 53rd Annual Conference on Decision and Control (CDC)
%D 2014
%F eprints:2480
%I IEEE
%K Optimization, Sensor networks, Linear systems
%P 2228-2233
%T Sparse solutions to the average consensus problem via L1-Norm regularization of the fastest mixing Markov-Chain problem
%U http://eprints.imtlucca.it/2480/
%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.
%Z 53rd Annual Conference on Decision and Control (CDC), held in Los Angeles (USA) 15-17 December 2014