Advertisement

Non-convex Invariants and Urgency Conditions on Linear Hybrid Automata

  • Stefano Minopoli
  • Goran Frehse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8711)

Abstract

Linear hybrid automata (LHAs) are of particular interest to formal verification because sets of successor states can be computed exactly, which is not the case in general for more complex dynamics. Enhanced with urgency, LHA can be used to model complex systems from a variety of application domains in a modular fashion. Existing algorithms are limited to convex invariants and urgency conditions that consist of a single constraint. Such restrictions can be a major limitation when the LHA is intended to serve as an abstraction of a model with urgent transitions. This includes deterministic modeling languages such as Matlab-Simulink, Modelica, and Ptolemy, since all their transitions are urgent. The goal of this paper is to remove these limitations, making LHA more directly and easily applicable in practice. We propose an algorithm for successor computation with non-convex invariants and closed, linear urgency conditions. The algorithm is implemented in the open-source tool PHAVer, and illustrated with an example.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Henzinger, T., Ho, P.H.: Automatic symbolic verification of embedded systems. IEEE Trans. Softw. Eng. 22, 181–201 (1996)CrossRefGoogle Scholar
  2. 2.
    Bagnara, R., Hill, P.M., Zaffanella, E.: The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Science of Computer Programming 72(1-2), 3–21 (2008)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Bauer, N., Kowalewski, S., Sand, G., Löhl, T.: A case study: Multi product batch plant for the demonstration of control and scheduling problems. In: Engell, S., Kowalewski, S., Zaytoon, J. (eds.) ADPM 2000, pp. 383–388. Shaker (2000)Google Scholar
  4. 4.
    van Beek, D.A., Reniers, M.A., Schiffelers, R.R.H., Rooda, J.E.: Foundations of a compositional interchange format for hybrid systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 587–600. Springer, Heidelberg (2007)Google Scholar
  5. 5.
    Behrmann, G., David, A., Larsen, K.G.: A tutorial on uppaal. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 200–236. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Benerecetti, M., Faella, M., Minopoli, S.: Automatic synthesis of switching controllers for linear hybrid systems: Safety control. TCS 493, 116–138 (2012)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Buck, J.T., Ha, S., Lee, E.A., Messerschmitt, D.G.: Ptolemy: A framework for simulating and prototyping heterogeneous systems. Ablex Publishing Corp. (1994)Google Scholar
  8. 8.
    Frehse, G., Le Guernic, C., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Frehse, G.: PHAVer: algorithmic verification of hybrid systems past HyTech. STTT 10(3), 263–279 (2008)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Gebremichael, B., Vaandrager, F.: Specifying urgency in timed i/o automata. In: SEFM 2005, pp. 64–74. IEEE Computer Society (2005)Google Scholar
  11. 11.
    Henzinger, T.A., Ho, P.H., Wong-Toi, H.: Hytech: the next generation. In: Proc. IEEE Real-Time Systems Symposium, p. 56. IEEE Computer Society (1995)Google Scholar
  12. 12.
    Henzinger, T.: The theory of hybrid automata. In: 11th IEEE Symp. Logic in Comp. Sci., pp. 278–292 (1996)Google Scholar
  13. 13.
    Ho, P.H.: Automatic Analysis of Hybrid Systems. Ph.D. thesis, Cornell University, technical Report CSD-TR95-1536 (August 1995)Google Scholar
  14. 14.
    MathWorks: Mathworks simulink: Simulation et model-based design (Mar 2014), http://www.mathworks.fr/products/simulink
  15. 15.
    Mattsson, S.E., Elmqvist, H., Otter, M.: Physical system modeling with Modelica. Control Engineering Practice 6(4), 501–510 (1998)CrossRefGoogle Scholar
  16. 16.
    Minopoli, S., Frehse, G.: Non-convex invariants and urgency conditions on linear hybrid automata. Tech. Rep. TR-2014-4, Verimag (April 2014)Google Scholar
  17. 17.
    Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: An approach to the description and analysis of hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, pp. 149–178. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  18. 18.
    Wong-Toi, H.: The synthesis of controllers for linear hybrid automata. In: IEEE Conf. Decision and Control, pp. 4607–4612. IEEE (1997)Google Scholar
  19. 19.
    De Wulf, M., Doyen, L., Raskin, J.-F.: Almost ASAP semantics: From timed models to timed implementations. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 296–310. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Stefano Minopoli
    • 1
  • Goran Frehse
    • 1
  1. 1.Centre ÉquationVERIMAGGiéresFrance

Personalised recommendations