  This paper proposes a game-theoretic approach to address the problem of
optimal sensor placement against an adversary in uncertain networked control
systems. The problem is formulated as a zero-sum game with two players, namely
a malicious adversary and a detector. Given a protected performance vertex, we
consider a detector, with uncertain system knowledge, that selects another
vertex on which to place a sensor and monitors its output with the aim of
detecting the presence of the adversary. On the other hand, the adversary, also
with uncertain system knowledge, chooses a single vertex and conducts a
cyber-attack on its input. The purpose of the adversary is to drive the attack
vertex as to maximally disrupt the protected performance vertex while remaining
undetected by the detector. As our first contribution, the game payoff of the
above-defined zero-sum game is formulated in terms of the Value-at-Risk of the
adversary's impact. However, this game payoff corresponds to an intractable
optimization problem. To tackle the problem, we adopt the scenario approach to
approximately compute the game payoff. Then, the optimal monitor selection is
determined by analyzing the equilibrium of the zero-sum game. The proposed
approach is illustrated via a numerical example of a 10-vertex networked
control system.
