  Cyber-physical systems (CPS) with reinforcement learning (RL)-based
controllers are increasingly being deployed in complex physical environments
such as autonomous vehicles, the Internet-of-Things(IoT), and smart cities. An
important property of a CPS is tolerance; i.e., its ability to function safely
under possible disturbances and uncertainties in the actual operation. In this
paper, we introduce a new, expressive notion of tolerance that describes how
well a controller is capable of satisfying a desired system requirement,
specified using Signal Temporal Logic (STL), under possible deviations in the
system. Based on this definition, we propose a novel analysis problem, called
the tolerance falsification problem, which involves finding small deviations
that result in a violation of the given requirement. We present a novel,
two-layer simulation-based analysis framework and a novel search heuristic for
finding small tolerance violations. To evaluate our approach, we construct a
set of benchmark problems where system parameters can be configured to
represent different types of uncertainties and disturbancesin the system. Our
evaluation shows that our falsification approach and heuristic can effectively
find small tolerance violations.
