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Edge Selection in Bilinear Dynamical Networks

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Document pages: 7 pages

Abstract: In large-scale networks, agents (e.g., sensors and actuators) and links(e.g., couplings and communication links) can be vulnerable to (cyber-)attacks.In this paper, we focus on continuous-time bilinear networks, where additivedisturbances model attack uncertainty on agents states (a.k.a. nodedisturbances) and multiplicative disturbances model attacks uncertainties oncouplings between agents states (a.k.a. link disturbances). We then investigatenetwork robustness notion in terms of the underlying digraph of the network,and structure of exogenous uncertainties attacks. Specifically, we define therobustness measure using the $ mathcal H 2$-norm of the network and calculateit in terms of the reachability Gramian of the bilinear system. the kernels ofthe Volterra series expansion of the state. The main result is that undercertain conditions, the measure is supermodular over the set of all possibleattacked links. The supermodular property facilitates the efficient solutionfinding of the optimization problem. We conclude the paper with a few examplesillustrating how different structures can make the system more or lessvulnerable to malicious attacks on links.

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