  We present a resource-planning game for cyber-security of networked control
systems (NCS). The NCS is assumed to be operating in closed-loop using a linear
state-feedback $\mathcal{H}_2$ controller. A zero-sum, two-player Stackelberg
game (SG) is developed between an attacker and a defender for this NCS. The
attacker aims to disable communication of selected nodes and thereby render the
feedback gain matrix to be sparse, leading to degradation of closed-loop
performance, while the defender aims to prevent this loss by investing in the
protection of targeted nodes. Both players trade their
$\mathcal{H}_2$-performance objectives for the costs of their actions. The
standard backward induction method is modified to determine a cost-based
Stackelberg equilibrium (CBSE) that saves the players' costs without degrading
the control performance. We analyze the dependency of a CBSE on the relative
budgets of the players as well as on the node "importance" order. Moreover, a
robust-defense method is developed for the realistic case when the defender is
not informed about the attacker's resources. The proposed algorithms are
validated using examples from wide-area control of electric power systems. It
is demonstrated that reliable and robust defense is feasible unless the
defender's resources are severely limited relative to the attacker's resources.
We also show that the proposed methods are robust to time-varying model
uncertainties and thus are suitable for long-term security investment in
realistic NCSs. Finally, we employ computationally efficient genetic algorithms
(GA) to compute the optimal strategies of the attacker and the defender in
realistic large power systems.
