  We present a moving target defense strategy to reduce the impact of stealthy
sensor attacks on feedback systems. The defender periodically and randomly
switches between thresholds from a discrete set to increase the uncertainty for
the attacker and make stealthy attacks detectable. However, the defender does
not know the exact goal of the attacker but only the prior of the possible
attacker goals. Here, we model one period with a constant threshold as a
Bayesian game and use the Bayesian Nash equilibrium concept to find the
distribution for the choice of the threshold in that period, which takes the
defender's uncertainty about the attacker into account. To obtain the
equilibrium distribution, the defender minimizes its cost consisting of the
cost for false alarms and the cost induced by the attack. We present a
necessary and sufficient condition for the existence of a moving target defense
and formulate a linear program to determine the moving target defense.
Furthermore, we present a closed-form solution for the special case when the
defender knows the attacker's goals. The results are numerically evaluated on a
four-tank process.
