Compositional abstractions of hybrid control systems

Abstraction is a natural way to hierarchically decompose the analysis and design of hybrid systems. Given a hybrid control system and some desired properties, one extracts an 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. We present a framework for abstraction that applies to abstract control systems capturing discrete, continuous, and hybrid systems. Parallel composition is presented in a categorical framework and an algorithm is proposed to construct abstractions of hybrid control systems. Finally, we show that our abstractions of hybrid systems are compositional.