  In this paper, we propose a data-driven approach to formally verify the
safety of (potentially) unknown discrete-time continuous-space stochastic
systems. The proposed framework is based on a notion of barrier certificates
together with data collected from trajectories of unknown systems. We first
reformulate the barrier-based safety verification as a robust convex problem
(RCP). Solving the acquired RCP is hard in general because not only the state
of the system lives in a continuous set, but also and more problematic, the
unknown model appears in one of the constraints of RCP. Instead, we leverage a
finite number of data, and accordingly, the RCP is casted as a scenario convex
problem (SCP). We then relate the optimizer of the SCP to that of the RCP, and
consequently, we provide a safety guarantee over the unknown stochastic system
with a priori guaranteed confidence. We apply our approach to an unknown room
temperature system by collecting sampled data from trajectories of the system
and verify formally that temperature of the room lies in a comfort zone for a
finite time horizon with a desired confidence.
