Data driven finite abstractions by simulation relations with probabilistic guarantees using regression trees

In this paper we propose a novel methodology to construct, given trajectories measured from a dynamical system, a finite abstraction by means of a transition system. We prove that our abstraction is a simulation of the original dynamical system, providing quantified probabilistic guarantees derived using the scenario approach. We test our methodology on a benchmark on hybrid systems showing that it strongly reduces the cardinality of the abstraction states with respect to a uniform grid, and is thus very promising for handling abstractions of large dimensional systems.