  This paper proposes a game-theoretic method to address the problem of optimal
detector placement in a networked control system under cyber-attacks. The
networked control system is composed of interconnected agents where each agent
is regulated by its local controller over unprotected communication, which
leaves the system vulnerable to malicious cyber-attacks. To guarantee a given
local performance, the defender optimally selects a single agent on which to
place a detector at its local controller with the purpose of detecting
cyber-attacks. On the other hand, an adversary optimally chooses a single agent
on which to conduct a cyber-attack on its input with the aim of maximally
worsening the local performance while remaining stealthy to the defender.
First, we present a necessary and sufficient condition to ensure that the
maximal attack impact on the local performance is bounded, which restricts the
possible actions of the defender to a subset of available agents. Then, by
considering the maximal attack impact on the local performance as a game
payoff, we cast the problem of finding optimal actions of the defender and the
adversary as a zero-sum game. Finally, with the possible action sets of the
defender and the adversary, an algorithm is devoted to determining the Nash
equilibria of the zero-sum game that yield the optimal detector placement. The
proposed method is illustrated on an IEEE benchmark for power systems.
