Centrality in Time-Delay Consensus Networks with Structured Uncertainties

Ghaedsharaf, Yaser; Siami, Milad; Somarakis, Christoforos; Motee, Nader

doi:10.48550/arxiv.1902.08514

Cited by 2 publications

(2 citation statements)

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“…Consensus [4], [11]- [16], on one hand, refers to the ability of the network nodes to asymptotically reach a common value over some quantities of interest. Many extensions of this problem include the study of robustness and performance of consensus networks in the presence of noise [12]- [14], timedelay [15], [16], and switching graph topology [16]. Synchronization [5], [8]- [10], [17]- [19], on the other hand, refers to the ability of network nodes to follow a commonly defined trajectory.…”

Section: Introductionmentioning

confidence: 99%

Coherence and Concentration in Tightly-Connected Networks

Min¹,

Pates²,

Mallada³

2021

Preprint

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The ability to achieve coordinated behaviorengineered or emergent-on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of the conditions under which agents within a network can reach an agreement (consensus) or develop coordinated behavior, such as synchronization. However, much less understood is the phenomenon of network coherence. Network coherence generally refers to nodes' ability in a network to have a similar dynamic response despite heterogeneity in their individual behavior. In this paper, we develop a general framework to analyze and quantify the level of network coherence that a system exhibits by relating coherence with a low-rank property of the system. More precisely, for a networked system with linear dynamics and coupling, we show that, as the network connectivity grows, the system transfer matrix converges to a rank-one transfer matrix representing the coherent behavior. Interestingly, the non-zero eigenvalue of such a rank-one matrix is given by the harmonic mean of individual nodal dynamics, and we refer to it as the coherent dynamics. Our analysis unveils the frequency-dependent nature of coherence and a non-trivial interplay between dynamics and network topology. We further show that many networked systems can exhibit similar coherent behavior by establishing a concentration result in a setting with randomly chosen individual nodal dynamics.

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Section: Introductionmentioning

confidence: 99%

Coherence and Concentration in Tightly-Connected Networks

Min¹,

Pates²,

Mallada³

2021

Preprint

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“…The centrality analysis of a time-delayed consensus network has been studied in [8] and a closed form of the node and link centralities in the presence of different noises in the network is offered. In [9] the authors have studied the convergence analysis of the time-delayed networks with linear dynamics and established a connection between their convergence rate and delay (in addition to the correlation it has with the largest eigenvalue of the graph).…”

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confidence: 99%

Centrality in Epidemic Networks with Time-Delay: A Decision-Support Framework for Epidemic Containment

Darabi

Siami

2021

2021 American Control Conference (ACC)

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During an epidemic, infectious individuals might not be detectable until some time after becoming infected. The studies show that carriers with mild or no symptoms are the main contributors to the transmission of a virus within the population. The average time it takes to develop the symptoms causes a delay in the spread dynamics of the disease. When considering the influence of delay on the disease propagation in epidemic networks, depending on the value of the time-delay and the network topology, the peak of epidemic could be considerably different in time, duration, and intensity. Motivated by the recent worldwide outbreak of the COVID-19 virus and the topological extent in which this virus has spread over the course of a few months, this study aims to highlight the effect of time-delay in the progress of such infectious diseases in the meta-population networks rather than individuals or a single population. In this regard, the notions of epidemic network centrality in terms of the underlying interaction graph of the network, structure of the uncertainties, and symptom development duration are investigated to establish a centrality-based analysis of the disease evolution. A traffic volume convex optimization method is then developed to control the outbreak by identifying the sub-populations with the highest centrality and then isolating them while maintaining the same overall traffic volume (motivated by economic considerations) in the meta-population level. The numerical results, along with the theoretical expectations, highlight the impact of time-delay as well as the importance of considering the worst-case scenarios in investigating the most effective methods of epidemic containment. I. INTRODUCTIONThe large-scale spread of an infectious disease occurs every few years and leads into serious crises before it eventually dies out [1]. The extend in which a high-speed epidemic continues depends mostly on first, the government interventions, and second, the existence of an effective treatment against the disease. In this regard, the study of epidemic propagation by network

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Centrality in Time-Delay Consensus Networks with Structured Uncertainties

Cited by 2 publications

References 20 publications

Coherence and Concentration in Tightly-Connected Networks

Coherence and Concentration in Tightly-Connected Networks

Centrality in Epidemic Networks with Time-Delay: A Decision-Support Framework for Epidemic Containment

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