A Game Theoretic Approach to Design a Resilient Controller For a Nonlinear Discrete System

In this paper, the problem of designing a cyber-resilient controller is studied for a class of nonlinear discrete systems subject to actuator attacks. We develop a coupled control design approach, which incorporates interaction between the intrusion detection system (IDS) and the attacker, with the controller design in the physical layer. In the considered cyber-attack scenario, the attacker attempts to first bypass the IDS to spoof the system actuator and then deteriorate the controller performance in the physical layer. The optimal attack strategy to deceive the IDS is obtained based on a zero-sum game in the detection layer. In the physical layer, it is assumed that the system has a secure compensator along with the actuator to deal with the injected attack values. Therefore, the controller and the compensator are designed based on the results of the game in the detection layer, and stochastic stability analysis and Lyapunov function methods are used to prove boundedness of the system state in the probabilistic sense. Finally, through numerical analysis of a representative example, the proposed design procedure is illustrated and its efficacy in maintaining robust stability of the cyber-physical system under actuator attacks is demonstrated.