Complete stealthy false data injection attacks in hypernetworked control systems

In this work, we study the problem of false data injection attacks in a control system where the units interact not only in pairs, but also in groups of a larger number of nodes. We use hypergraphs, and more specifically simplicial complexes, to model the interactions in the system that, therefore, we indicate as a hypernetworked control system. Attacks have the aim of destabilizing the system solution, which, in the absence of attacks, is instead stable. We characterize the properties that are satisfied by destabilizing attacks, namely unboundedness, stealthiness, and complete stealthiness. Finally, we provide some numerical examples confirming our theoretical results.