How Sensor Attacks Transfer Across Lie Groups
Sensor spoofing analysis in cyber-physical systems is predominantly confined to linear state spaces, where an attack's persistence implies the existence of an integrator somewhere in the loop. We extend this insight to a commutativity condition on Lie groups, where noncommutative dynamics can distort sensor attacks, exposing nominally stealthy attacks by complex maneuvers. We present a geometric framework characterizing when a sensor attack can transfer across operating conditions, preserving both its physical impact and stealthiness. We prove that successful transfer requires the attack to commute with the flow (a Lie bracket condition), isolating transferable attacks to an invariant subspace. For small deviations from transferable attacks, our decomposition theorem reveals a fundamental asymmetry: the flow's Adjoint action distorts the physical impact of the bracket-violating component. Furthermore, even if the attack's impact isn't distorted, the subsequent residual could be. Finally, we demonstrate how turning maneuvers on a Dubins unicycle collapse the transferable subspace to a single direction, verifying that imperfect attacks remain within theoretical detection bounds.