Departmental Papers (CIS)

Document Type

Journal Article

Date of this Version

July 2000

Comments

Copyright 2000 IEEE. Reprinted from Proceedings of the IEEE, Volume 88, Issue 7, July 2000, pages 971-984.
Publisher URL: http://dx.doi.org/10.1109/5.871304

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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 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.

Keywords

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

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Date Posted: 30 April 2005

This document has been peer reviewed.