  We study the performance of perception-based control systems in the presence
of attacks, and provide methods for modeling and analysis of their resiliency
to stealthy attacks on both physical and perception-based sensing.
Specifically, we consider a general setup with a nonlinear affine physical
plant controlled with a perception-based controller that maps both the physical
(e.g., IMUs) and perceptual (e.g., camera) sensing to the control input; the
system is also equipped with a statistical or learning-based anomaly detector
(AD). We model the attacks in the most general form, and introduce the notions
of attack effectiveness and stealthiness independent of the used AD. In such
setting, we consider attacks with different levels of runtime knowledge about
the plant. We find sufficient conditions for existence of stealthy effective
attacks that force the plant into an unsafe region without being detected by
any AD. We show that as the open-loop unstable plant dynamics diverges faster
and the closed-loop system converges faster to an equilibrium point, the system
is more vulnerable to effective stealthy attacks. Also, depending on runtime
information available to the attacker, the probability of attack remaining
stealthy can be arbitrarily close to one, if the attacker's estimate of the
plant's state is arbitrarily close to the true state; when an accurate estimate
of the plant state is not available, the stealthiness level depends on the
control performance in attack-free operation.
