Actuator Security Indices Based on Perfect Undetectability: Computation, Robustness, and Sensor Placement

We propose an actuator security index that can be used to localize and protect vulnerable actuators in a networked control system. Particularly, the security index of an actuator equals to the minimum number of sensors and actuators that need to be compromised, such that a perfectly undetectable attack against that actuator can be conducted. We derive a method for computing the index in small-scale systems and show 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 index is NP-hard to compute, sensitive with respect to system variations, and based on the assumption that the attacker knows the entire system model. To overcome these difficulties, a robust security index is introduced. The robust index can characterize actuators vulnerable in any system realization, can be calculated in polynomial time, and can be related to limited model knowledge attackers. Additionally, we analyze two sensor placement problems with the objective to increase the robust indices. We show that the problems have submodular structures, so their suboptimal solutions with performance guarantees can be computed in polynomial time. Finally, we illustrate the theoretical developments through examples.