Assessing Node Criticality in Dynamical Distributed Systems

In this paper we characterize the vulnerability of the different elements of a geographically dispersed and networked LTI discrete-time dynamical system by taking the perspective of an attacker aiming at steering the system state towards an undesirable configuration via the injection of control signals at selected subsystems. Specifically, we assume the attacker aims at directly intervening on the minimum number of subsystems and at injecting the minimum energy signal that would steer the state towards the target adverse configuration, while minimizing the number of steps required to reach such a configuration. Such three conflicting objectives generate a Pareto front of solutions, and the vulnerability of each subsystem is evaluated in terms of the frequency with which each node is attacked in the solutions belonging to the Pareto front. Such a vulnerability assessment can be the base to prioritize the protection resources to be allocated at each subsystem.