Haifa Verification Conference

Hardware and Software: Verification and Testing pp 19-35 | Cite as

Abstraction-Based Parameter Synthesis for Multiaffine Systems

  • Sergiy Bogomolov
  • Christian Schilling
  • Ezio Bartocci
  • Gregory Batt
  • Hui Kong
  • Radu Grosu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9434)

Abstract

Multiaffine hybrid automata (MHA) represent a powerful formalism to model complex dynamical systems. This formalism is particularly suited for the representation of biological systems which often exhibit highly non-linear behavior. In this paper, we consider the problem of parameter identification for MHA. We present an abstraction of MHA based on linear hybrid automata, which can be analyzed by the SpaceEx model checker. This abstraction enables a precise handling of time-dependent properties. We demonstrate the potential of our approach on a model of a genetic regulatory network and a myocyte model.

References

  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. Theor. Comput. Sci. 138(1), 3–34 (1995)CrossRefMathSciNetMATHGoogle 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. Sci. Comput. Program. 72(1), 3–21 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bartocci, E., Bortolussi, L., Nenzi, L.: A temporal logic approach to modular design of synthetic biological circuits. In: Gupta, A., Henzinger, T.A. (eds.) CMSB 2013. LNCS, vol. 8130, pp. 164–177. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  4. 4.
    Bartocci, E., Corradini, F., Di Berardini, M.R., Entcheva, E., Smolka, S., Grosu, R.: Modeling and simulation of cardiac tissue using hybrid I/O automata. Theor. Comput. Sci. 410(410), 3149–3165 (2009)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Batt, G., Belta, C., Weiss, R.: Temporal logic analysis of gene networks under parameter uncertainty. IEEE Trans. Autom. Control 53, 215–229 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Batt, G., Yordanov, B., Weiss, R., Belta, C.: Robustness analysis and tuning of synthetic gene networks. Bioinformatics 23(18), 2415–2422 (2007)CrossRefGoogle Scholar
  7. 7.
    Belta, C., Habets, L.: Controlling a class of nonlinear systems on rectangles. IEEE Trans. Autom. Control 51(11), 1749–1759 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cherry, E.M., Fenton, F.H.: Visualization of spiral and scroll waves in simulated and experimental cardiac tissue. New J. Phys. 10, 125016 (2008)CrossRefGoogle Scholar
  9. 9.
    Dang, T., Donzé, A., Maler, O., Shalev, N.: Sensitive state-space exploration. In: CDC, pp. 4049–4054 (2008)Google Scholar
  10. 10.
    Dreossi, T., Dang, T.: Parameter synthesis for polynomial biological models. In: Proceedings of HSCC 2014: The 17th International Conference on Hybrid Systems: Computation and Control, HSCC 2014, pp. 233–242. ACM, New York, NY, USA (2014)Google Scholar
  11. 11.
    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
  12. 12.
    Gao, S., Avigad, J., Clarke, E.M.: \(\delta \)-complete decision procedures for satisfiability over the reals. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 286–300. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  13. 13.
    Grosu, R., Batt, G., Fenton, F.H., Glimm, J., Le Guernic, C., Smolka, S.A., Bartocci, E.: From cardiac cells to genetic regulatory networks. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 396–411. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  14. 14.
    Habets, L.C.G.J.M., Collins, P.J., van Schuppen, J.H.: Reachability and control synthesis for piecewise-affine hybrid systems on simplices. IEEE Trans. Autom. Control 51(6), 938–948 (2006)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Kloetzer, M., Belta, C.: Reachability analysis of multi-affine systems. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 348–362. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  16. 16.
    Liu, B., Kong, S., Gao, S., Zuliani, P., Clarke, E.M.: Parameter synthesis for cardiac cell hybrid models using delta-decisions. CoRR, abs/1407.1524 (2014)Google Scholar
  17. 17.
    Myers, C.J.: Engineering Genetic Circuits. Chapman and Hall/CRC (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sergiy Bogomolov
    • 1
  • Christian Schilling
    • 2
  • Ezio Bartocci
    • 3
  • Gregory Batt
    • 4
  • Hui Kong
    • 1
  • Radu Grosu
    • 3
  1. 1.IST AustriaKlosterneuburgAustria
  2. 2.University of FreiburgFreiburg im BreisgauGermany
  3. 3.Vienna University of TechnologyViennaAustria
  4. 4.INRIA Paris-RocquencourtParisFrance

Personalised recommendations