Centrality in Time-Delay Consensus Networks with Structured Uncertainties
This work provides a theoretical framework for quantifying the influence of agents and communication links in consensus networks with time-delay and structured uncertainties, which is relevant for network analysis and control design.
The paper defines centrality measures for time-delay consensus networks with structured uncertainties using the H2-norm, deriving explicit formulas that depend on time-delay, graph Laplacian, and noise covariance. It shows that centrality measures can be highly sensitive to time-delay, leading to counterintuitive rankings of agents and links.
We investigate notions of network centrality in terms of the underlying coupling graph of the network, structure of exogenous uncertainties, and communication time-delay. Our focus is on time-delay linear consensus networks, where uncertainty is modeled by structured additive noise on the dynamics of agents. The centrality measures are defined using the $\mathcal H_2$-norm of the network. We quantify the centrality measures as functions of time-delay, the graph Laplacian, and the covariance matrix of the input noise. Several practically relevant uncertainty structures are considered, where we discuss two notions of centrality: one w.r.t intensity of the noise and the other one w.r.t coupling strength between the agents. Furthermore, explicit formulas for the centrality measures are obtained for all types of uncertainty structures. Lastly, we rank agents and communication links based on their centrality indices and highlight the role of time-delay and uncertainty structure in each scenario. Our counter intuitive grasp is that some of centrality measures are highly volatile with respect to time-delay.