Reachability analysis of interconnected systems under stealthy attacks

This article investigates the reachable set of interconnected systems subject to stealthy attacks corrupting sensor measurements and control signals, with both the residuals and distributed interconnection estimation errors used for attack detection. When the reachable set of the interconnected system is unbounded, we firstly prove the equivalence between analyzing the system states and analyzing the estimation errors induced by attacks. Then the necessary and sufficient conditions for the reachable set being unbounded are derived for the finite and infinite time horizon, respectively. When the reachable set of the interconnected system is bounded, an outer approximation of the reachable sets is obtained with a given probability level. Moreover, the volume of the approximation and the distance to the dangerous-safe boundary are adopted to evaluate the safety of the system, respectively. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approaches.