Cyber-Physical Systems With Multiple Denial-of-Service Attackers: A Game-Theoretic Framework

Cyber-physical systems (CPSs) under denial-of-service (DoS) attacks are investigated in the present work. Besides multiple controllers in the physical-layer, there exist multiple DoS attackers in the cyber-layer congesting communication channels simultaneously, which deteriorates the control performance of the physical process. To tackle this coupling decision making process, a game-theoretic framework is established to characterize the interaction among the multiple controllers and the multiple DoS attackers. Specifically, a static cooperative game is formulated for the collaboration among the multiple DoS attackers in the cyber-layer, while a noncooperative differential game for the competition among the multiple controllers in the physical world, and the probabilistic data packet dropout determined by the coordination of DoS attackers plays as the bond connecting these two games. Subsequently, a selection scheme based on Pareto front is proposed to achieve an agreement of all DoS attackers without any preference information, and robust feedback Nash equilibrium strategies with respect to environmental disturbances and packet dropouts are constructed for all controllers. Finally, a quadruple-tank system is employed to demonstrate the effectiveness and applicability of the proposed results.