A Hierarchical Game Approach to the Coupled Resilient Control of CPS against Denial-of-Service Attack

In this paper, the resilient control problem has been studied for cyber-physical systems (CPSs) under the Denial-of-Service (DoS) attack. The term resilience is interpreted as the ability to be robust to the physical layer external disturbance and defending against cyber layer DoS attacks. The overall resilient control system is described by a hierarchical game, where the cyber security issue is modeled as a zerosum matrix game, and physical H∞ minimax control problem is described by a zero-sum dynamic game. In virtue of the reinforcement learning method, the defense/attack policy in the cyber layer can be obtained. Additionally, the physical layer control strategy can be obtained by using the dynamical programming method. The criteria to judge whether a cyber system is capable of protecting the underlying control system are provided as well. Finally, the proposed method is verified by a numerical example.