Skip to main content

Discrete-Time Refinement of Hybrid Automata

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2289))

Abstract

Notations like hybrid automata are highly useful in the development process of hybrid systems to document requirements in early design steps. When it comes to implementation a part of the requirements will be realized in software in a discrete-time manner.We therefore study suficient conditions which ensure that an automaton operating in discrete-time refines a hybrid automaton with its underlying continuous time model. Our notion of refinement provides that vital properties which have been established for the hybrid automaton also hold for its refinement. Furthermore, we outline a method how to derive a discrete-time refinement from a hybrid automaton.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Alur, C. Courcoubetis, N. Halbwachs, T.A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3–34, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  2. R. Alur, R. Grosu, I. Lee, and O. Sokolsky. Compositional refinement of hierarchical hybrid systems. In Proc. of HSCC’01, LNCS 2034. Springer-Verlag, 2001.

    Google Scholar 

  3. M. Fränzle. Analysis of hybrid systems:An ounce of realism can save an infinity of states. In Proc. of Computer Science Logic (CSL’99), LNCS 1683. Springer, 1999.

    Google Scholar 

  4. R. Grosu, T. Stauner, and M. Broy. A modular visual model for hybrid systems. In Proc. of FTRTFT’98, LNCS 1486. Springer-Verlag, 1998.

    Google Scholar 

  5. V. Gupta, T.A. Henzinger, and R. Jagadeesan. Robust timed automata. In Proc. of HART 97, LNCS 1201. Springer-Verlag, 1997.

    Google Scholar 

  6. T.A. Henzinger and J.-F. Raskin. Robust undecidability of timed and hybrid systems. In Proc. of HSCC’00, LNCS 1790. Springer-Verlag, 2000.

    Google Scholar 

  7. D. V. Hung and P. H. Giang. Sampling semantics of duration calculus. In Proceedings of FTRTFT’ 96, LNCS 1135. Springer-Verlag, 1996.

    Google Scholar 

  8. M. K. Jain. Numerical Solution of Differential Equations. Wiley Eastern Ltd., New Delhi, 1979.

    MATH  Google Scholar 

  9. Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems. Springer-Verlag, 1992.

    Google Scholar 

  10. K. Ogata. Discrete-Time Control Systems. Prentice-Hall, 1987.

    Google Scholar 

  11. D. Sinclair. Using an object-oriented methodology to bring a hybrid system from initial concept to formal definition. In Proc. Int. Workshop on Hybrid and Real-Time Systems (HART’97), LNCS 1201. Springer-Verlag, 1997.

    Google Scholar 

  12. T. Stauner. Systematic Development of Hybrid Systems. PhD thesis, Technische Universität München, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Stauner, T. (2002). Discrete-Time Refinement of Hybrid Automata. In: Tomlin, C.J., Greenstreet, M.R. (eds) Hybrid Systems: Computation and Control. HSCC 2002. Lecture Notes in Computer Science, vol 2289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45873-5_32

Download citation

  • DOI: https://doi.org/10.1007/3-540-45873-5_32

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43321-7

  • Online ISBN: 978-3-540-45873-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics