Resilient Output Feedback Tube-Based MPC for Cyber-Physical Systems Under Hybrid Attacks

This paper proposes a resilient output feedback tube-based model predictive control (MPC) approach for constrained cyber-physical systems (CPSs) to handle the impact of stochastic hybrid attacks, where the hybrid attacks include false data injection (FDI) attacks and denial-of-service (DoS) attacks that occur in the sensor-controller (S-C) and controller-actuator (C-A) channels, respectively. The anomalous behavior of the attacker is revealed by the designed attack detector and comparator, which provide alert signals that guide the primary and auxiliary controllers to collaboratively generate control inputs as well as a nominal trajectory. The tolerable attack duration is determined by using the concept of $\mu $ -step robust positive invariant ( $\mu $ -RPI) set, which limits the size of the deviation between the observer and the nominal trajectory under the hybrid attacks. Robust constraint satisfaction and robust asymptotic stability are ensured by restricting the state of the system to a tube centered on a nominal trajectory that converges gradually to the origin, and theoretical guarantees are provided. Finally, the effectiveness of the designed algorithm is validated through a supply chain model, which includes comparisons with an inelastic scheme.