TY  - CHAP
N2  - 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.
SP  - 2228
A1  - Gnecco, Giorgio
A1  - Morisi, Rita
A1  - Bemporad, Alberto
PB  - IEEE
SN  - 978-1-4799-7746-8 
UR  - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7039729&isnumber=7039338
AV  - none
TI  - Sparse solutions to the average consensus problem via L1-Norm regularization of the fastest mixing Markov-Chain problem
Y1  - 2014/12//
KW  - Optimization
KW  -  Sensor networks
KW  -  Linear systems
T2  - Proceedings of the 53rd Annual Conference on Decision and Control (CDC)
EP  - 2233
ID  - eprints2480
N1  - 53rd Annual Conference on Decision and Control (CDC), held in Los Angeles (USA) 15-17 December 2014 
ER  -