Data-Driven Abstraction of Monotone Systems

In this paper, we introduce an approach for data-driven abstraction of monotone dynamical systems. First, we present an approach to find the optimal approximation of the dynamics of an unknown system by a set-valued map based on a set of transitions generated by the system. Then we show that the dynamical system induced by the introduced map is equivalent (in the sense of alternating bisimulation) to a finite state transition system which can be used to synthesize controllers using the well-established symbolic control techniques. We show the effectiveness of the approach on a safety controller synthesis problem.