Dynamic Defense Resource Allocation for Minimizing Unsupplied Demand in Cyber-Physical Systems Against Uncertain Attacks

Cyber-attacks in cyber-physical systems (CPS) are receiving much attention due to the pervasive use of communication in essential services. If cyber components in CPS are compromised by attackers, the ability to maintain stability of the physical system is lost, and performance disruptions may occur. Vulnerability analysis allows quantifying the impact of attacks based on the damage cost model. Yet, existing works partially account for uncertainties in cyber-attacks and may provide inadequate support to decision making. This paper proposes a framework for optimal defense resource allocation for minimizing unsupplied demand of CPS under uncertain cyber-attacks. The vulnerability model of cyber components is described by an attacker-defender two-stage min-max game. The unavailability of cyber components causes the loss of performance of the monitored physical components. Uncertainties in the most probable attack time and in the accuracy of its estimate by the defender are considered. Numerical studies identify the optimum strategies in terms of protection and redundancy allocation of cyber components, and demonstrate that the contest intensity largely affects the two-stage game. Furthermore, if uncertainties increase, the system damage costs also increase and the defensive resource allocation strategies converge to a constant one due to the defender's lack of information about the attack.