Compositional abstractions of hybrid control systems

Abstraction is a natural way to hierarchically decompse the analysis and design of hybrid systems. Given a hybrid control system and some desired properties, one extracts and abstracted system while preserving the properties of interest. Abstractions of purely discrete systems is a mature area, whereas abstractions of continuous systems is a recent activity. In this paper we present a framework for abstraction that applies to discrete, continuous, and hybrid syustems. We introduce a composition operator that allows to build complex hybrid systems from simpler ones and show compatibility between abstractions and this compositional operator. Besides unifying the existing methodologies we also propose constructions to obtain abstractions of hybrid control systems.