Constrained Differential Games for Secure Decision-Making Against Stealthy Attacks

The problem of defending cyber-physical systems in noisy environments under malicious, stealthy actuator attacks, is considered. Both the attacker and the defender compute their open-loop policies iteratively over a predefined period. Due to the information asymmetry between the players, their decisions are derived through two separate constrained differential games. In finding optimal strategies, Pontryagin's minimum principle is employed to obtain the defense policy that optimizes the system performance and the attack policy that manipulates the future evolution of the system while optimally exploiting the information asymmetry present in the game.