Vulnerability of Network Synchronization Processes: A Minimum Energy Perspective

We study the vulnerability of a linear network synchronization process to intrusion at a single network component, from a graph-theoretic perspective. Specifically, we model the intruder as seeking to move the state of the synchronization process to an undesirable value or set via a local actuation. We measure the network vulnerability in terms of the minimum or expected minimum actuation energy required of the adversary to achieve the goal, which is related to the inverse of the controllability Gramian for the process and statistics defined thereof (e.g., its trace and determinant). Using explicit formulas for the Gramian inverse and its associated statistics together with algebraic graph-theory concepts, we then develop structural and graph-theoretic characterizations of the energy-based vulnerability measures.