Resilience Distributed MPC for Dynamically Coupled Multiple Cyber–Physical Systems Subject to Severe Attacks

This article proposes a resilient distributed model predictive control (DMPC) algorithm for a class of constrained dynamically coupled multiple cyber-physical systems (CPSs) subject to bounded additive disturbances. The algorithm is designed to address severe attacks on the forward controller-actuator (C-A) channel, the feedback sensor-controller (S-C) channel, and the channels between subsystems, without any prior information about the intruder available to the defender. To mitigate the negative effects of intruders, we consider a one-step time delay strategy in the local model predictive controller design. This strategy allows the generated controller data to be checked for acceptability before use. To ensure constraint satisfaction for an infinite-horizon MPC problem while accounting for the unknown duration of attacks, we develop a set of minimally conservative constraints in the open-loop control mode using a constraint tightening technique. Moreover, we obtain an equivalent finite number of constraints for the infinite-horizon problem to ensure recursive feasibility. To prevent tampered data from affecting control performance, a detector module is designed to decide whether data is used by its receiver. It is shown that the closed-loop system is uniformly ultimate boundedness (UUB) under any admissible attack scenario and disturbance realization. Finally, the effectiveness of the proposed algorithm is validated by a case study.