Iterative Algorithms for Assessing Network Resilience Against Structured Perturbations

• Published in: IEEE transactions on control of network systems Vol. 9; no. 4; pp. 1816 - 1827
• Main Authors: Liu, Shenyu, Martinez, Sonia, Cortes, Jorge
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.12.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation algorithms; Eigenvalues and eigenfunctions; Energy levels; Heuristic algorithms; Iterative algorithms; Iterative methods; Linear systems; network systems; Perturbation; Perturbation methods; Resilience; Sparse matrices; spectral analysis; Stability analysis; Time invariant systems; Topology
• ISSN: 2325-5870; 2372-2533
• DOI: 10.1109/TCNS.2022.3165509

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.