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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 analyzed 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.
abstraction, decidability, hybrid systems, logic, model checking, discrete systems, temporal logic, continuous dynamics, discrete abstractions, discrete systems, o-minimal hybrid systems, rectangular hybrid systems, temporal logic, timed hybrid systems
Date Posted: 30 April 2005
This document has been peer reviewed.