Algebraic Connectivity Control and Maintenance in Multi-Agent Networks under Attack

TL;DR

This paper develops distributed protocols to enhance and maintain the algebraic connectivity of multi-agent networks under cyber-attacks, using local link modifications and random regular graph constructions, validated through theoretical proofs and simulations.

Contribution

It introduces two novel distributed protocols for increasing network connectivity under attack, one with proven convergence and the other validated via spectral analysis and simulations.

Findings

Protocols effectively maintain high connectivity despite attacks.

The coordinated protocol converges to the desired topology.

Both protocols outperform existing algorithms in simulations.

Abstract

This paper studies the problem of increasing the connectivity of an ad-hoc peer-to-peer network subject to cyber-attacks targeting the agents in the network. The adopted strategy involves the design of local interaction rules for the agents to locally modify the graph topology by adding and removing links with neighbors. Two distributed protocols are presented to boost the algebraic connectivity of the network graph beyond $k-2\sqrt{k-1}$ where $k\in \mathbb{N}$ is a free design parameter; these two protocols are achieved through the distributed construction of random (approximate) regular graphs. One protocol leverages coordinated actions between pairs of neighboring agents and is mathematically proven to converge to the desired graph topology. The other protocol relies solely on the uncoordinated actions of individual agents and it is validated by a spectral analysis through Monte-Carlo simulations. Numerical simulations offer a comparative analysis with other state-of-the-art algorithms, showing the ability of both proposed protocols to maintain high levels of connectivity despite attacks carried out with full knowledge of the network structure, and highlighting their superior performance.