Stochastic game approach for replay attack detection

The existing tradeoff between control system performance and the detection rate for replay attacks highlights the need to provide an optimal control policy that balances the security overhead with control cost. We employ a finite horizon, zero-sum, nonstationary stochastic game approach to minimize the worst-case control and detection cost, and obtain an optimal control policy for switching between control-cost optimal (but nonsecure) and secure (but cost-suboptimal) controllers in presence of replay attacks. To formulate the game, we quantify game parameters using knowledge of the system dynamics, controller design and utilized statistical detector. We show that the optimal strategy for the system exists, and present a suboptimal algorithm used to calculate the system's strategy by combining robust game techniques and a finite horizon stationary stochastic game algorithm. Our approach can be generalized for any system with multiple finite cost, time-invariant linear controllers/estimators/intrusion detectors.