  As control systems become increasingly more complex, there exists a pressing
need to find systematic ways of verifying them. To address this concern, there
has been significant work in developing test generation schemes for black-box
control architectures. These schemes test a black-box control architecture's
ability to satisfy its control objectives, when these objectives are expressed
as operational specifications through temporal logic formulae. Our work extends
these prior, model based results by lower bounding the probability by which the
black-box system will satisfy its operational specification, when subject to a
pre-specified set of environmental phenomena. We do so by systematically
generating tests to minimize a Lipschitz continuous robustness measure for the
operational specification. We demonstrate our method with experimental results,
wherein we show that our framework can reasonably lower bound the probability
of specification satisfaction.
