  This paper proposes an actuator security index based on the definition of
perfect undetectability. This index can help a control system operator to
localize the most vulnerable actuators in the networked control system, which
can then be secured. Particularly, the security index of an actuator equals the
minimum number of sensors and actuators that needs to be compromised, such that
a perfectly undetectable attack against that actuator can be conducted. A
method for computing the index for small scale networked control systems is
derived, and it is shown that the index can potentially be increased by placing
additional sensors. The difficulties that appear once the system is of a large
scale are then outlined: the problem of calculating the index is NP--hard, the
index is vulnerable to system variations, and it is based on the assumption
that the attacker knows the entire model of the system. To overcome these
difficulties, a robust security index is introduced. The robust index can be
calculated in polynomial time, it is unaffected by the system variations, and
it can be related to both limited and full model knowledge attackers.
Additionally, we analyze two sensor placement problems with the objective to
increase the robust indices. We show that both of these problems have
submodular structures, so their suboptimal solutions with performance
guarantees can be obtained in polynomial time. Finally, the theoretical
developments are illustrated through numerical examples.

Systems and Control