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International Hybrid Systems Workshop

HS 1997: Hybrid Systems V pp 238–250Cite as

Time-Deterministic Hybrid Transition Systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1567))

Abstract

Hybrid transition systems in their full generality describe continuous behaviour by a set of equations in each mode - an algebraic or differential equation for each state variable in terms of inputs and other state variables. Each discrete transition may be taken according to a (non-deterministic) time constraint.

In this paper we restrict this model to time-deterministic discrete transitions. Thus, every transition is guarded by a condition g and has a fixed delay t. Different transitions may have different delays (including zero), but progress is enforced after the delay. Using this restriction and a composition operator which uses union of mode sets we then prove certain compositionality properties. In particular, that the parallel composition of two subsystems produces a system whose semantics is defined in terms of semantics of its constituents provided that it has a run. The restriction is well-justified in a large class of control applications where the complex mode-changing software is realised as a synchronous program.

This work was supported by the Esprit LTR project 22703 (SYRF) and the Swedish board for technical research (TFR).

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References

  1. M. Abadi and L. Lamport. Conjoining Specifications. ACM transactions on Programming Languages and Systems, 1995.

    Google Scholar 

  2. 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. Journal of Theoretical Computer Science, 138:3–34, 1995.

    Article  MathSciNet  Google Scholar 

  3. R. Alur, T.A. Henzinger, and E. Sontag, editors. Proc. of the DIMACS International Workshop on Verification and Control of Hybrid Systems, LNCS 1066. Springer Verlag, 1996.

    Google Scholar 

  4. S. Bensalem, P. Caspi, and C. Parent-Vigouroux. Handling Data-Flow Programs in PVS. Technical report, VERIMAG, 1996. Available through http://www-verimag.imag.fr//SYNCHRONE/SYRF/HTML97/a341.html.

  5. A. Benveniste. Compositional and Uniform Modelling of Hybrid Systems. In Alur et al. [3], pages 41–51.

    Chapter  Google Scholar 

  6. G. Berry. The Foundations of Esterel. In Proofs, Languages and Interaction: Essays in Honour of Robin Milner. MIT Press, 1998. To appear.

    Google Scholar 

  7. M. S. Branicky. Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis, Laboratory for Information and Decision Systems, Massachusetts Institute of Technoloy, June 1995. Dissertation no. LIDS-TH-2304.

    Google Scholar 

  8. J.W. de Bakker, C. Huizing, W.P. de Roever, and G. Rozenberg, editors. Real-Time: Theory in Practice, Proc. REX workshop 1991. Springer Verlag, LNCS 600, 1992.

    Google Scholar 

  9. B. Dutertre and V. Stavridou. Formal Requirements Analysis of an Avionics Control System. IEEE Transactions on Software Engineering, 25(5): 267–278, May 1997.

    Article  Google Scholar 

  10. N. Halbwachs. Synchronous Programming of Reactive Systems. Kluwer Academic Publishers, 1993.

    Google Scholar 

  11. N. Halbwachs, F. Lagnier, and P. Raymond. Synchronous observers and the verification of reactive systems. In M. Nivat, C. Rattray, T. Rus, and G. Scollo, editors, Third Int. Conf. on Algebraic Methodology and Software Technology, AMAST’93, Twente, June 1993. Workshops in Computing, Springer Verlag.

    Google Scholar 

  12. Y. Kesten, Z. Manna, and A. Pnueli. Verifying Clocked Transition Systems. In Alur et al. [3], pages 13–40.

    Chapter  Google Scholar 

  13. H. Langmaack, W.-P. de Roever, and J. Vytopil, editors. Proc. of the 3rd. International Conference on Formal Techniques in Real-time and Fault-tolerant Systems, LNCS 863. Springer Verlag, 1994.

    Google Scholar 

  14. N. Lynch, R. Segala, F. Vaandrager, and H.B. Weinberg. Hybrid I/O Automata. In Alur et al. [3], pages 496–510.

    Chapter  Google Scholar 

  15. O. Maler, Z. Manna, and A. Pnueli. From Timed to Hybrid Systems. In de Bakker et al. [8], pages 447–484.

    Google Scholar 

  16. Z. Manna and A. Pnueli. Models for Reactivity. Acta Informatica, 30:609–678, 1993.

    Article  MathSciNet  Google Scholar 

  17. S. Nadjm-Tehrani and J-E. Strömberg. From Physical modelling to Compositional models of Hybrid Systems. In Langmaack et al. [13], pages 583–604.

    Chapter  Google Scholar 

  18. S. Nadjm-Tehrani and J-E. Strömberg. Proving Dynamic Properties in an Aerospace Application. In Proc. of the 16th International Symposium on Real-time Systems, pages 2–10. IEEE Computer Society Press, December 1995.

    Google Scholar 

  19. S. Nadjm-Tehrani and J-E. Strömberg. Verification of Dynamic Properties in an Aerospace application. Formal Methods in System Design, 1998. To appear.

    Google Scholar 

  20. The SYRF Project. Work package 7 Deliverable: Analog/discrete synchronous design Annex A.7.1a. Available from http://www-verimag.imag.fr//SYNCHRONE/SYRF/HTML97/a71.html, December 1997.

  21. J. Sifakis and S. Yovine. Compositional Specification of Timed Systems. In Proc. of the 13th annual Symposium on Theoretical Aspects of Computer Science, STAC’’96, LNCS 1046, pages 347–359. Springer Verlag, 1996.

    MATH  Google Scholar 

  22. J.-E. Strömberg, S. Nadjm-Tehrani, and J. Top. Switched Bond Graphs as Frontend to Formal Verification of Hybrid Systems. In Alur et al. [3], pages 282–293.

    Chapter  Google Scholar 

  23. J.E. Strö;mberg and S. Nadjm-Tehrani. On Discrete and Hybrid Representation of Hybrid Systems. In Proceedings of the SCS International Conference on Modeling and Simulation (ESM’ 94), pages 1085–1089, Barcelona, June 1994.

    Google Scholar 

  24. M. Westhead and J. Hallam. Modelling Hybrid Systems as the Limit of Discrete Computational Processes. In Proceedings of the International Conference on Robotics and Automation. IEEE, 1996.

    Google Scholar 

  25. M. Westhead and S. Nadjm-Tehrani. Verification of Embedded Systems using Synchronous Observers. In Proceedings of the 4th International Conference on Formal Techniques in Real-time and Fault-tolerant Systems, LNCS 1135, pages 405–419. Springer Verlag, September 1996.

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer & Information Science, Linköping University, S-581 83, Linköping, Sweden

    Simin Nadjm-Tehrani

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  1. Simin Nadjm-Tehrani
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Panos Antsaklis  & Michael Lemmon  & 

  2. Hynomics Corporation, 10632 NE 37th Circle, Building 23, Kirkland, WA, 98033, USA

    Wolf Kohn

  3. Department of Mathematics, Cornell University, 217, White Hall, Ithaca, NY, 14853, USA

    Anil Nerode

  4. Electronic Research Laboratory, University of California at Berkeley, 253 Cory Hall, Berkeley, CA, 94720, USA

    Shankar Sastry

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© 1999 Springer-Verlag Berlin Heidelberg

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Nadjm-Tehrani, S. (1999). Time-Deterministic Hybrid Transition Systems. In: Antsaklis, P., Lemmon, M., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems V. HS 1997. Lecture Notes in Computer Science, vol 1567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49163-5_13

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  • DOI: https://doi.org/10.1007/3-540-49163-5_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65643-2

  • Online ISBN: 978-3-540-49163-7

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