Iterative Algorithms for Assessing Network Resilience Against Structured Perturbations

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 stru...

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Published inIEEE transactions on control of network systems Vol. 9; no. 4; pp. 1816 - 1827
Main Authors Liu, Shenyu, Martinez, Sonia, Cortes, Jorge
Format Journal Article
LanguageEnglish
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
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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.
AbstractList 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.
Author Cortes, Jorge
Martinez, Sonia
Liu, Shenyu
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Snippet This article studies network resilience against structured additive perturbations to its topology. We consider dynamic networks modeled as linear...
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SubjectTerms 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
Title Iterative Algorithms for Assessing Network Resilience Against Structured Perturbations
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