  As the complexity of control systems increases, the need for systematic
methods to guarantee their efficacy grows as well. However, direct testing of
these systems is oftentimes costly, difficult, or impractical. As a result, the
test and evaluation ideal would be to verify the efficacy of a system simulator
and use this verification result to make a statement on true system
performance. This paper formalizes that performance translation for a specific
class of desired system behaviors. In that vein, our contribution is twofold.
First, we detail a variant on existing Bayesian Optimization Algorithms that
identifies minimal upper bounds to maximization problems, with some minimum
probability. Second, we use this Algorithm to $i)$ lower bound the minimum
simulator robustness and $ii)$ upper bound the expected deviance between true
and simulated systems. Then, for the specific class of desired behaviors
studied, we leverage these bounds to lower bound the minimum true system
robustness, without directly testing the true system. Finally, we compare a
high-fidelity ROS simulator of a Segway, with a significantly noisier version
of itself, and show that our probabilistic verification bounds are indeed
satisfied.
