Geometrical Characterization of Sensor Placement for Cone-Invariant and Multi-Agent Systems against Undetectable Zero-Dynamics Attacks

Undetectable attacks are an important class of malicious attacks threatening the security of cyber-physical systems, which can modify a system's state but leave the system output measurements unaffected, and hence cannot be detected from the output. This paper studies undetectable attacks on cone-invariant systems and multi-agent systems. We first provide a general characterization of zero-dynamics attacks, which characterizes fully undetectable attacks targeting the non-minimum phase zeros of a system. This geometrical characterization makes it possible to develop a defense strategy seeking to place a minimal number of sensors to detect and counter the zero-dynamics attacks on the system's actuators. The detect and defense scheme amounts to computing a set containing potentially vulnerable actuator locations and nodes, and a defense union for feasible placement of sensors based on the geometrical properties of the cones under consideration.