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Data-Driven Abstraction of Monotone Systems

In this paper, we introduce an approach for the data-driven abstraction of monotone dynamical systems. First, we introduce a set-valued simulating map, which over-approximates the dynamics of an unknown monotone system, using only a set of transitions generated by it. We establish the minimality of the introduced simulating map. Then, we show that the system, with this map as its transition relation, is equivalent (in the sense of alternating bisimulation) to a finite-state system. This equivalence enables the use of well-established symbolic control techniques to synthesize controllers. We show the effectiveness of the approach on a safety controller synthesis problem.