  The abstraction of dynamical systems is a powerful tool that enables the
design of feedback controllers using a correct-by-design framework. We
investigate a novel scheme to obtain data-driven abstractions of discrete-time
stochastic processes in terms of richer discrete stochastic models, whose
actions lead to nondeterministic transitions over the space of probability
measures. The data-driven component of the proposed methodology lies in the
fact that we only assume samples from an unknown probability distribution. We
also rely on the model of the underlying dynamics to build our abstraction
through backward reachability computations. The nondeterminism in the
probability space is captured by a collection of Markov Processes, and we
identify how this model can improve upon existing abstraction techniques in
terms of satisfying temporal properties, such as safety or reach-avoid. The
connection between the discrete and the underlying dynamics is made formal
through the use of the scenario approach theory. Numerical experiments
illustrate the advantages and main limitations of the proposed techniques with
respect to existing approaches.
