Vulnerability of continuous-time network synchronization processes: A minimum energy perspective

Abstract

We characterize the vulnerability of a linear network synchronization process to intrusion by an adversary that can actuate a single network component. Specifically, we model the intruder as seeking to move the state of the synchronization process to an undesirable value or set (which may or may not be known to system operators) via a local actuation. We evaluate the network vulnerability in terms of the whether or not the intruder can achieve its goal, and also the minimum actuation energy (or expected minimum energy, if the goal is unknown) required of the adversary to achieve the goal. We formalize that the required energy is related to the inverse of the controllability Gramian for the process, and statistics defined thereof (e.g., its trace and determinant). We then obtain explicit formulas for the Gramian inverse and its associated statistics. These explicit formulae yield interesting structural and graphtheoretic characterizations of the energy-based vulnerability measures.

Local open- and closed-loop manipulation of multi-agent networks

“…The analysis of the eigenvalues follows immediately from the classical work of Chua [12]. The eigenvector analysis turns out to be more intricate because of the possibility for non-simple eigenvalue, but closely follows the analyses given in [13,3]. Since this is the case, we simply present the result in the following lemma and corollary, relegating the proofs to Appendices A and B.…”

“…In general, one finds that the uncontrollability of the DIN dynamics results from the presence of certain sub-structures in the network graph. For instance, partial symmetry of the graph Ψ with respect to certain vertices, presence of identically-interconnected vertex sets, and presence of bottleneck node sets in the graph can all lead to uncontrollability (see [13,3] for details). However, typical or generic network graphs do not have these sub-structures.…”

“…On one hand, a single agent may be leveraged by a stakeholder to monitor system health or enact a mission plan. On the other hand, an adversary may be able to manipulate the entire network via an attack on a single agent [1,2,3]. In a similar vein, large-scale infrastructure networks (e.g., the electric power grid [4,5]) are becoming increasingly susceptible to global manipulation from local components, as these components are provided with a growing level of cyberintelligence and connectivity.…”

Cyber- Threat Assessment for the Air Traffic Management System: A Network Controls Approach

“…Formal algebraic analyses of these problems can be completed by applying and building on control-theory techniques. These analyses then give a starting point for developing topological insights into threat impact, using recent results that tie network structure to reachability and robustness levels [17][18][19]. They also bring forth interesting new questions regarding reachability and robustness in networks with layered structures, as well as reachability using sign-definite inputs.…”

“…Relative to this literature, the main innovation here is to study the spatiotemporal impacts of disruptions from a graph-theory and network-controls perspective, and to develop models and analyses for meshed cyber, traffic, and weather dynamics. The research described here also connects to a broader effort to evaluate threats to cyber-physical systems from a network-controls perspective, but achieves a keener analysis focused on the specific models used in air traffic management (e.g., [19,[27][28][29]). …”