Discrete abstractions of hybrid systems

TLDR

Hybrid systems combine discrete and continuous state changes, and for analysis it is useful to abstract them while preserving relevant properties and hiding irrelevant details. The paper surveys and unifies results on discrete abstractions of hybrid systems from both continuous‑dynamics‑restricted and discrete‑dynamics‑restricted perspectives. The authors analyze classes of hybrid systems that can be abstracted to purely discrete systems while preserving all temporal‑logic properties. They show that such abstractions are possible for two categories of systems: those with restricted continuous dynamics (timed and rectangular) and those with restricted discrete dynamics (o‑minimal).

Abstract

A hybrid system is a dynamical system with both discrete and continuous state changes. For analysis purposes, it is often useful to abstract a system in a way that preserves the properties being analysed while hiding the details that are of no interest. We show that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic. The classes that permit discrete abstractions fall into two categories. Either the continuous dynamics must be restricted, as is the case for timed and rectangular hybrid systems, or the discrete dynamics must be restricted, as is the case for o-minimal hybrid systems. In this paper, we survey and unify results from both areas.