  This paper studies the sensor placement problem in a networked control system
for improving its security against cyber-physical attacks. The problem is
formulated as a zero-sum game between an attacker and a detector. The
attacker's decision is to select $f$ nodes of the network to attack whereas the
detector's decision is to place $f$ sensors to detect the presence of the
attack signals. In our formulation, the attacker minimizes its visibility,
defined as the system $L_2$ gain from the attack signals to the deployed
sensors' outputs, and the detector maximizes the visibility of the attack
signals. The equilibrium strategy of the game determines the optimal locations
of the sensors. The existence of Nash equilibrium for the attacker-detector
game is studied when the underlying connectivity graph is a directed or an
undirected tree. When the game does not admit a Nash equilibrium, it is shown
that the Stackelberg equilibrium of the game, with the detector as the game
leader, can be computed efficiently. Finally, the attacker-detector game is
studied in a cooperative adaptive cruise control algorithm for vehicle
platooning problem. The existence of Nash equilibrium is investigated for both
directed and undirected platoons and the effect of the position of the
reference vehicle on the game value is studied. Our results show that, under
the optimal sensor placement strategy, an undirected topology provides a higher
security level for a networked control system compared with its corresponding
directed topology.
