Vulnerability Analysis against Stealthy Integrity Attacks for Nonlinear Systems

This paper considers the vulnerability issues of a class of nonlinear systems to stealthy integrity attacks. To characterize the stealthiness of the attack, a forward-invariant set for the system output is introduced. Additionally, a safety set for the system state is established to evaluate the attack’s safety. Our analysis demonstrates that the nonlinear system is non-vulnerable to strictly stealthy integrity attacks if it is uniformly observable. When the uniform observability property is not satisfied, we show that the considered class of nonlinear systems is not vulnerable to stealthy integrity attacks when an output-to-state safe barrier function is admitted. Moreover, for nonlinear systems that are vulnerable to stealthy integrity attacks, we analytically show how these are parameterized. Our analytic results are validated with numerical simulations that demonstrate the applicability of the presented analysis.