Iterative algorithms for assessing network resilience against structured perturbations

Shenyu Liu, Sonia Martínez and Jorge Cortés
IEEE Transactions on Control of Networked Systems, 9 (4) (2022) 1816-1827

Abstract:

This article studies network resilience against structured additive perturbations to its topology. We consider dynamic networks modeled as linear time-invariant systems subject to perturbations of bounded energy satisfying specific sparsity and entry-wise constraints. Given an energy level, the structured pseudospectral abscissa captures the worst-possible perturbation an adversary could employ to destabilize the network, and the structured stability radius is the maximum energy in the structured perturbation that the network can withstand without becoming unstable. Building on a novel characterization of the worst-case structured perturbation, we propose iterative algorithms that efficiently compute the structured pseudospectral abscissa and structured stability radius. We provide theoretical guarantees of the local convergence of the algorithms and illustrate their efficacy and accuracy on several network examples.

File: (ArXiv version)

Bib-tex entry:

@article{SL-SM-JC:18-tcps,
author = {S. Liu and S. Mart{\'\i}nez and J. Cort\'es},
title = {Iterative algorithms for assessing network resilience against structured perturbations },
journal= {IEEE Transactions on Control of Network Systems},
pages = {1816-1827},
volume = {9},
number = {4},
year = {2022}
}