Gnecco, Giorgio and Morisi, Rita and Bemporad, Alberto
*Sparse Solutions to the Average Consensus Problem via Various Regularizations of the Fastest Mixing Markov-Chain Problem.*
IEEE Transactions on Network Science and Engineering, 2 (3).
pp. 97-111.
ISSN 2327-4697
(2015)

## Abstract

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.

Item Type: | Article |
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Identification Number: | 10.1109/TNSE.2015.2479086 |

Uncontrolled Keywords: | Artificial neural networks; Convergence; Convex functions; Eigenvalues and eigenfunctions; Optimization; Symmetric matrices; Wireless sensor networks; Consensus; Fastest Mixing Markov-Chain problem; Optimization; Regularization; Sparsity |

Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science T Technology > T Technology (General) |

Research Area: | Computer Science and Applications |

Depositing User: | Caterina Tangheroni |

Date Deposited: | 19 Oct 2015 09:22 |

Last Modified: | 19 Oct 2015 09:22 |

URI: | http://eprints.imtlucca.it/id/eprint/2774 |

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