Resilient Model Predictive Control of Cyber-Physical Systems Under DoS Attacks

This article presents a resilient model predictive control (MPC) framework to attenuate adverse effects of denial-of-service (DoS) attacks for cyber-physical systems (CPSs), where the system dynamics is modeled by a linear time-invariant system. A DoS attacker targets at blocking the controller to actuator (C-A) communication channel by launching adversarial jamming signals. We show that, in order to guarantee exponential stability of the closed-loop system, several conditions for resilient MPC should be satisfied. And these established conditions are explicitly related to the duration of DoS attacks and MPC parameters such as the prediction horizon and the terminal constraint. Two key techniques, including the $\mu$-step positively invariant set and the modified initial feasible set are exploited for achieving exponential stability in the presence of DoS attacks. Moreover, the maximum allowable duration of the DoS attacker is also obtained by using the $\mu$-step positively invariant set. Finally, the effectiveness of the proposed MPC algorithm is verified by simulated studies and comparisons.