Inherent attack tolerance properties of model predictive control under DoS attacks

We consider the inherent attack tolerance properties of resilient model predictive control (R-MPC) for cyber–physical systems (CPSs) modeled by discrete linear time-invariant (LTI) systems subjected to limited disruptions. In this paper, the relationship between the maximum allowable duration of Denial-of-Service (DoS) attacks, namely attacks that disrupt both sensor to controller (S–C) and controller to actuator (C–A) communication channels, and the upper bound of disturbances is deduced at length. Moreover, to achieve robust recursive feasibility and closed-loop stability of the system, we discuss that MPC with state, control and terminal constraints has a certain degree of inherent attack tolerance concerning the DoS attack duration and parameters like system matrices and the nominal terminal set. Finally, numerical simulation is given to substantiate the effectiveness of the proposed approach.