A cyber-security investment game for networked control systems

We formulate a resource-planning game between an attacker and a defender of a Network Control System (NCS). We consider the network to be operating in closed-loop with a linear quadratic regulator (LQR). We construct a general-sum, two-player, mixed strategy (MS) game, where the attacker attempts to destroy communication equipment of some nodes, and thereby render the LQR feedback gain matrix to be sparse, leading to degradation of closed-loop performance. The defender, on the other hand, aims to prevent this loss. Both players trade their control performance objectives for the cost of their actions. A Mixed Strategy Nash Equilibrium (MSNE) of the game represents the allocation of the players' respective resources for attacking or protecting the important network nodes. Numerical results for the New England power system model demonstrate that reliable defense is feasible unless the cost of attack is much smaller than the cost of protection per generator.