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We present a resource-planning game for cyber-security of networked controlsystems (NCS). The NCS is assumed to be operating in closed-loop using a linearstate-feedback $\mathcal{H}_2$ controller. A zero-sum, two-player Stackelberggame (SG) is developed between an attacker and a defender for this NCS. Theattacker aims to disable communication of selected nodes and thereby render thefeedback gain matrix to be sparse, leading to degradation of closed-loopperformance, while the defender aims to prevent this loss by investing in theprotection of targeted nodes. Both players trade their$\mathcal{H}_2$-performance objectives for the costs of their actions. Thestandard backward induction method is modified to determine a cost-basedStackelberg equilibrium (CBSE) that saves the players' costs without degradingthe control performance. We analyze the dependency of a CBSE on the relativebudgets of the players as well as on the node "importance" order. Moreover, arobust-defense method is developed for the realistic case when the defender isnot informed about the attacker's resources. The proposed algorithms arevalidated using examples from wide-area control of electric power systems. Itis demonstrated that reliable and robust defense is feasible unless thedefender's resources are severely limited relative to the attacker's resources.We also show that the proposed methods are robust to time-varying modeluncertainties and thus are suitable for long-term security investment inrealistic NCSs. Finally, we employ computationally efficient genetic algorithms(GA) to compute the optimal strategies of the attacker and the defender inrealistic large power systems.

A Robust Stackelberg Game for Cyber-Security Investment in Networked Control Systems