Game-Theory-Based Optimal Defense for Cyberspace Attacks in Industrial Cyber–Physical Systems With Information Uncertainties

When applying the game-theoretic approach to find the optimal strategy for industrial cyber-physical systems defenders, most existing work assumes both the system states (e.g., for a power grid system, the system state captures which buses are compromised) and the attacker’s instant actions are observable and can be used to make the decision for the defender’s next move. Also, the reward and expected utilities are calculated based on the most likely system state and attack action. However, there is uncertainty in determining the system state and attack actions as the attack unfolds in the system in practice. This work shows that such an approximation is non-optimal in determining the defense strategy. Instead, we propose a framework that models the uncertainty in the system state and attack action. We derive the defender’s optimal strategy under such uncertainty by calculating the expected utilities across different action spaces and redefining the immediate reward within the deep learning algorithm based on the expected utilities and our estimation of the probabilistic distribution of the system state and attack action, ultimately employing the agent system for learning and generating the optimal defense strategy. The simulation experiments are carried out based on the generic industrial cyber-physical system testbed and the numerical results confirmed that the proposed solution can improve the defender’s expected utilities by 38.8% compared to the state-of-the-art.