International Conference on Formal Modeling and Analysis of Timed Systems

FORMATS 2015: Formal Modeling and Analysis of Timed Systems pp 1-9 | Cite as

Verification and Control of Probabilistic Rectangular Hybrid Automata

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9268)


Hybrid systems are characterised by a combination of discrete and continuous components. In many application areas for hybrid systems, such as vehicular control and systems biology, stochastic behaviour is exhibited. This has led to the development of stochastic extensions of formalisms, such as hybrid automata, for the modelling of hybrid systems, together with their associated verification and controller synthesis algorithms, in order to allow reasoning about quantitative properties such as “the vehicle’s speed will reach 50kph within 10 seconds with probability at least 0.99”. We consider verification and control of probabilistic rectangular hybrid automata, which generalise the well-known class of rectangular hybrid automata with the possibility of representing random behaviour of the discrete components of the system, permitting the modelling of the likelihood of faults, choices in randomised algorithms and message losses. Furthermore, we will also consider how probabilistic rectangular hybrid automata can be used as abstract models for more general classes of stochastic hybrid systems.


Model Check Hybrid System Markov Decision Process Stochastic Game Hybrid Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. TCS 138(1), 3–34 (1995)CrossRefMATHGoogle Scholar
  2. 2.
    Assouramou, J., Desharnais, J.: Analysis of non-linear probabilistic hybrid systems. In: Proc. QAPL 2011. EPTCS, vol. 57, pp. 104–119 (2011)Google Scholar
  3. 3.
    Baier, C., Größer, M., Leucker, M., Bollig, B., Ciesinski, F.: Controller synthesis for probabilistic systems (extended abstract). In: Levy, J.-J., Mayr, E.W., Mitchell, J.C. (eds.) TCS 2004. IFIP, vol. 155, pp. 493–506. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Baier, C., Katoen, J.-P.: Principles of model checking. MIT Press (2008)Google Scholar
  5. 5.
    Büchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Transactions of the AMS 138, 295–311 (1969)CrossRefMATHGoogle Scholar
  6. 6.
    Bujorianu, M.L., Lygeros, J.: Reachability questions in piecewise deterministic Markov processes. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 126–140. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  7. 7.
    Chatterjee, K., Henzinger, T.A.: A survey of stochastic omega-regular games. J. Comput. Syst. Sci. 78(2), 394–413 (2012)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Clarke, E., Grumberg, O., Peled, D.: Model checking. MIT Press (2001)Google Scholar
  9. 9.
    David, A., Du, D., Larsen, K.G., Legay, A., Mikucionis, M., Poulsen, D.B., Sedwards, S.: Statistical model checking for stochastic hybrid systems. In: Proc. HSB 2012. EPTCS, vol. 92, pp. 122–136 (2012)Google Scholar
  10. 10.
    Davis, M.H.A.: Markov Models and Optimization. Chapman and Hall (1993)Google Scholar
  11. 11.
    Doyen, L., Henzinger, T.A., Raskin, J.-F.: Automatic rectangular refinement of affine hybrid systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 144–161. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  12. 12.
    Forejt, V., Kwiatkowska, M., Norman, G., Trivedi, A.: Expected reachability-time games. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 122–136. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  13. 13.
    Fränzle, M., Hahn, E.M., Hermanns, H., Wolovick, N., Zhang, L.: Measurability and safety verification for stochastic hybrid systems. In: Proc. HSCC 2011, pp. 43–52. ACM (2011)Google Scholar
  14. 14.
    Fränzle, M., Teige, T., Eggers, A.: Engineering constraint solvers for automatic analysis of probabilistic hybrid automata. J. Log. Algebr. Program. 79(7), 436–466 (2010)CrossRefMathSciNetMATHGoogle Scholar
  15. 15.
    Gregersen, H., Jensen, H.E.: Formal design of reliable real time systems. Master’s thesis, Department of Mathematics and Computer Science, Aalborg University (1995)Google Scholar
  16. 16.
    Hahn, E.M.: Model checking stochastic hybrid systems. Dissertation, Universität des Saarlandes (2013)Google Scholar
  17. 17.
    Henzinger, T.A.: The theory of hybrid automata. In: Proc. LICS 1996, pp. 278–292. IEEE (1996)Google Scholar
  18. 18.
    Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: Algorithmic analysis of nonlinear hybrid systems. IEEE TSE 43, 540–554 (1998)MathSciNetMATHGoogle Scholar
  19. 19.
    Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? J. Comput. Syst. Sci. 57(1), 94–124 (1998)CrossRefMathSciNetMATHGoogle Scholar
  20. 20.
    Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Verifying quantitative properties of continuous probabilistic timed automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 123–137. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  21. 21.
    Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. TCS 286, 101–150 (2002)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Lafferriere, G., Pappas, G., Sastry, S.: O-minimal hybrid systems. Mathematics of Control, Signals, and Systems 13(1), 1–21 (2000)CrossRefMathSciNetMATHGoogle Scholar
  23. 23.
    Laroussinie, F., Sproston, J.: State explosion in almost-sure probabilistic reachability. IPL 102(6), 236–241 (2007)CrossRefMathSciNetMATHGoogle Scholar
  24. 24.
    Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proc. POPL 1989, pp. 179–190. ACM Press (1989)Google Scholar
  25. 25.
    Ramadge, P.J., Wonham, W.M.: Supervisory control of a class of discrete-event processes. SIAM Journal of Control and Optimization 25(1), 206–230 (1987)CrossRefMathSciNetMATHGoogle Scholar
  26. 26.
    Raskin, J.-F.: An introduction to hybrid automata. In: Handbook of Networked and Embedded Control Systems, pp. 491–518. Birkhäuser (2005)Google Scholar
  27. 27.
    Sproston, J.: Decidable model checking of probabilistic hybrid automata. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 31–45. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  28. 28.
    Sproston, J.: Model Checking for Probabilistic Timed and Hybrid Systems. PhD thesis, School of Computer Science, University of Birmingham (2001)Google Scholar
  29. 29.
    Sproston, J.: Discrete-time verification and control for probabilistic rectangular hybrid automata. In: Proc. QEST 2011, pp. 79–88. IEEE (2011)Google Scholar
  30. 30.
    Sproston, J.: Exact and approximate abstraction for classes of stochastic hybrid systems. In: Proc. AVOCS 2014. Electronic Communications of the EASST, pp. 79–88 (2014)Google Scholar
  31. 31.
    Tkachev, I., Mereacre, A., Katoen, J.-P., Abate, A.: Quantitative automata-based controller synthesis for non-autonomous stochastic hybrid systems. In: Proc. HSCC 2013, pp. 293–302. ACM (2013)Google Scholar
  32. 32.
    Vladimerou, V., Prabhakar, P., Viswanathan, M., Dullerud, G.E.: STORMED hybrid systems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 136–147. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  33. 33.
    Zhang, L., She, Z., Ratschan, S., Hermanns, H., Hahn, E.M.: Safety verification for probabilistic hybrid systems. European Journal of Control 18(6), 572–587 (2012)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversity of TurinTurinItaly

Personalised recommendations