A Game-Theoretic Two-Stage Stochastic Programing Model to Protect CPS against Attacks

Securing Cyber-Physical Systems (CPS) against cyber-attacks is a challenging problem as it requires continuously checking control and measurement signals for errors at runtime. The assignment of check blocks to check those signals must be performed using the available but possibly incomplete or uncertain information and within the delay bounds dictated by the control loop. Moreover, the assignment should remain unpredictable against an adversary who is able to observe/probe the assignment placed and adapt her attack methods accordingly. Due to the large number of potential check blocks that can be assigned, their varying effectiveness in detecting a wide range of cyber-attacks, and the uncertainty on the exact number of signals that need to be checked and protected, finding such strategic assignment is a critical endeavor. This paper presents two-stage stochastic programming models for equipping the CPS control loops with the proper check blocks to secure them. The formulation is based on a game theoretical approach to enable the defender to find an optimal randomized (i.e., mixed strategy) assignment of check blocks while abiding to the control-loop constraints. The models incorporate uncertainty in the number of signals to be checked/protected and capture various degrees of overhead in the operation of the check blocks. We illustrate the superiority of our results, in terms of the value of the stochastic solution, when compared to other assignment strategies. We validate our results through a Simulink-based model for a component in the operation of an autonomous vehicle.