A Worst-Case Approach to Safety and Reference Tracking for Cyber-Physical Systems Under Network Attacks

In this technical note, the safety and reference tracking control problems for cyber-physical systems (CPSs) equipped with authenticated communication channels are addressed. In this class of CPSs, network attacks can break the feedback loop at two different points for an arbitrarily long period. In this scenario, we design a novel control architecture that, by taking a worst-case approach, aims to preserve the safety of the systems while minimizing, whenever possible, the tracking performance degradation. On the plant side, a local safety controller is designed to take care of attacks on the actuation channel. In particular, given a finite number of predetermined admissible safe equilibrium points, this unit exploits a Voronoi partition of the state space and a family of dual-model set-theoretic model predictive controllers to safely confine, in a finite number of steps, the system into the closest robust control invariant region. On the other hand, on the controller side, the reference tracking controller operations are enhanced with an add-on module in charge of dealing with attack occurrences on the measurement channel. Specifically, by leveraging the Voronoi partition used on the plant’s side and reachability arguments, the objective of this unit is to reduce the performance loss by allowing a supervised system evolution until the best outcome in terms of tracking is achieved. The obtained theoretical results are proved and the solution’s effectiveness is shown through a simulation example.