Resiliency of Nonlinear Control Systems to Stealthy Sensor Attacks

In this work, we focus on analyzing vulnerability of nonlinear dynamical control systems to stealthy sensor attacks. We define the notion of stealthy attacks in the most general form by leveraging Neyman-Pearson lemma. Specifically, an attack is considered to be stealthy if it is stealthy from (i.e., undetected by) any intrusion detector – i.e., the probability of the detection is not better than a random guess. We then provide a sufficient condition under which a nonlinear control system is vulnerable to stealthy attacks, in terms of moving the system to an unsafe region due to the attacks. In particular, we show that if the closed-loop system is incrementally exponentially stable while the open-loop plant is incrementally unstable, then the system is vulnerable to stealthy yet impactful attacks on sensors. Finally, we illustrate our results on a case study.