Skip to main content
SpringerLink
Log in

Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations

  • Conference paper
  • First Online:
Hybrid Systems: Computation and Control (HSCC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1569))

Included in the following conference series:

Abstract

This paper presents a computational technique for verifying properties of hybrid systems with arbitrary continuous dynamics. The approach is based on the computation of approximating automata, which are finite-state approximations to the (possibly infinite-state) discretetrace transition system for the hybrid system. The fundamental computation in the generation of approximating automata is the mapping of sets of continuous states to the boundaries of the location invariants. This mapping is computed by intersecting flow pipes, the sets of reachable states for continuous systems, with the invariant boundaries. Flow pipes are approximated by sequences of overlapping convex polygons. The paper presents an application of the computational procedure to a benchmark hybrid system, a batch evaporator.

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Alur, T.A. Henzinger, and P.-H. Ho. Automatic symbolic verification of embedded systems. IEEE Trans. on Software Engineering, 22(3):181–201, Mar 1996.

    Article  Google Scholar 

  2. A. Chutinan and B.H. Krogh. Computing approximating automata for a class of hybrid systems. submitted to Mathematical Modeling of Systems: Special Issue on Discrete Event Models of Continuous Systems, 1997.

    Google Scholar 

  3. A. Chutinan and B.H. Krogh. Computing approximating automata for a class of linear hybrid systems. In Hybrid Systems V, Lecture Notes in Computer Science. Springer-Verlag, 1998.

    MATH  Google Scholar 

  4. A. Chutinan and B.H. Krogh. Computing polyhedral approximations to dynamic flow pipes. submitted to 37 th IEEE Conference on Decision and Control: Invited Session on Synthesis and Verification of Controllers for Hybrid Systems, 1998.

    Google Scholar 

  5. E. Clarke, O. Grumberg, and D. Long. Verification tools for finite-state concurrent systems. In Proceedings of A Decade of Concurrency: Reflections and Perspectives, pages 124–175, REX School/Symposium, Noordwijkerhout, The Netherlands, 1–4 June 1993. Springer-Verlag, Berlin, Germany, 1994.

    Google Scholar 

  6. T.A. Henzinger. Hybrid automata with finite bimulations. In Z. Fülöp and F. Gécseg, editors, ICALP 95: Automata, Languages, and Programming, pages 324–335. Springer-Verlag, 1995.

    Google Scholar 

  7. T.A. Henzinger. The theory of hybrid automata. In Proceedings of the 11th Annual Symposium on Logic in Computer Science, pages 278–292. IEEE Computer Society Press, 1996. Invited tutorial.

    Google Scholar 

  8. S. Kowalewski and O. Stursberg. The batch evaporator: A benchmark example for safety analysis of processing systems under logic control. submitted to: 4th Int. Workshop on Discrete Event Systems (WODES’ 98), Cagliari (Italy), August 1998.

    Google Scholar 

  9. B.H. Krogh and A. Chutinan. Hybrid systems: Modeling and control. In P.M. Frank, editor, Advances in Control. Springer-Verlag, 1999. To appear.

    Google Scholar 

  10. G. Lafferriere, G. J. Pappas, and S. Sastry. Hybrid systems with finite bisimulations. Technical Report UCB/ERL M98/15, University of California at Berkeley, April 1998.

    Google Scholar 

  11. G. Lafferriere, G. J. Pappas, and S. Yovine. Decidable hybrid systems. Technical Report UCB/ERL M98/39, University of California at Berkeley, June 1998.

    Google Scholar 

  12. Feng Zhao. Automatic Analysis and Synthesis of Controllers for Dynamical Systems Based on Phase-Space Knowledge. PhD thesis, MIT Artificial Intelligence Laboratory, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213-8390, USA

    Alongkrit Chutinan & Bruce H. Krogh

Authors
  1. Alongkrit Chutinan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bruce H. Krogh
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computing Science Institute, University of Nijmegen, P.O. Box 9010, 6500, GL, Nijmegen, The Netherlands

    Frits W. Vaandrager

  2. CWI, P.O. Box 94079, 1090, GB, Amsterdam, The Netherlands

    Jan H. van Schuppen

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chutinan, A., Krogh, B.H. (1999). Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations. In: Vaandrager, F.W., van Schuppen, J.H. (eds) Hybrid Systems: Computation and Control. HSCC 1999. Lecture Notes in Computer Science, vol 1569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48983-5_10

Download citation

  • DOI: https://doi.org/10.1007/3-540-48983-5_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65734-7

  • Online ISBN: 978-3-540-48983-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation