Structural Analysis and Design for Security Against Actuator Stealthy Attacks in Uncertain Systems

This paper considers the existence of stealthy integrity attacks for uncertain cyber-physical systems from a geometric point of view. We derive geometric structural conditions for the existence of stealthy integrity attacks and deduce the minimal actuator communication channels that, when protected, no stealthy integrity attacks exists. To examine different knowledge disclosure conditions for the attacker, we consider: (a) the attacker has full knowledge of the system linear terms but only the structure of the uncertain term, and (b) the attacker only knows the structures of the linear terms and the uncertain non-linear term. For scenario (a), the obtained existence condition of stealthy integrity attacks is that the uncertainty is decoupled with the maximal output-zeroing controlled-invariant subspace. In scenario (b), a graph is used to describe the uncertain system and we show that the existence of stealthy attacks is only possible if the uncertainty is decoupled with the fixed maximal output-zeroing controlled-invariant subspace. For each disclosure scenario, we deduce the minimum actuator communication channels to protect for guaranteeing the absence of stealthy integrity attacks. Our results are validated with a numerical example.