On the properties of optimal weak links in consensus networks

Makan Fardad; Xi Zhang; Fu Lin; Mihailo R. Jovanovic

doi:10.1109/CDC.2014.7039712

On the properties of optimal weak links in consensus networks

Makan Fardad, Xi Zhang, Fu Lin, Mihailo R. Jovanovic

Department of Electrical Engineering & Computer Science

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study consensus networks in which each node updates its state by taking a weighted average of the states of its neighbors. Our objective is to determine the optimal set of weak links whose addition to the network maximally improves the efficiency of reaching consensus. Allocating a small amount of resources to the entire network with which new links can be created, we employ a perturbation method to cast this problem as a linear program. We demonstrate that the set of optimal weak links is sparse and, based on extensive numerical experiments, conjecture that they are also long-range. Examples are provided to illustrate the utility of our developments.

Original language	English (US)
Article number	7039712
Pages (from-to)	2124-2129
Number of pages	6
Journal	Unknown Journal
Volume	2015-February
Issue number	February
DOIs	https://doi.org/10.1109/CDC.2014.7039712
State	Published - 2014

Keywords

Convex optimization
linear programming
long-range links
opinion dynamics
perturbation analysis
social networks
sparsity

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/CDC.2014.7039712

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AB - We study consensus networks in which each node updates its state by taking a weighted average of the states of its neighbors. Our objective is to determine the optimal set of weak links whose addition to the network maximally improves the efficiency of reaching consensus. Allocating a small amount of resources to the entire network with which new links can be created, we employ a perturbation method to cast this problem as a linear program. We demonstrate that the set of optimal weak links is sparse and, based on extensive numerical experiments, conjecture that they are also long-range. Examples are provided to illustrate the utility of our developments.

KW - Convex optimization

KW - linear programming

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KW - opinion dynamics

KW - perturbation analysis

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On the properties of optimal weak links in consensus networks

Abstract

Keywords

ASJC Scopus subject areas

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