Skip to main content
SpringerLink
Log in

Multi-objective Parameter Synthesis in Probabilistic Hybrid Systems

  • Conference paper
  • First Online:
Formal Modeling and Analysis of Timed Systems (FORMATS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9268))

Abstract

Technical systems interacting with the real world can be elegantly modelled using probabilistic hybrid automata (PHA). Parametric probabilistic hybrid automata are dynamical systems featuring hybrid discrete-continuous dynamics and parametric probabilistic branching, thereby generalizing PHA by capturing a family of PHA within a single model. Such system models have a broad range of applications, from control systems over network protocols to biological components. We present a novel method to synthesize parameter instances (if such exist) of PHA satisfying a multi-objective bounded horizon specification over expected rewards. Our approach combines three techniques: statistical model checking of model instantiations, a symbolic version of importance sampling to handle the parametric dependence, and SAT-modulo-theory solving for finding feasible parameter instances in a multi-objective setting. The method provides statistical guarantees on the synthesized parameter instances. To illustrate the practical feasibility of the approach, we present experiments showing the potential benefit of the scheme compared to a naive parameter exploration approach.

This work is funded by the EU FP7 projects MoVeS, SENSATION and AMBI, by the DFG through the collaborative research center SFB-TR 14 AVACS, and by the John Fell OUP Research Fund.

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. Bartlett, P.L., Mendelson, S.: Rademacher and gaussian complexities: Risk bounds and structural results. J. of Machine Learning Research 3, 463–482 (2003)

    MathSciNet  MATH  Google Scholar 

  2. Benedikt, M., Lenhardt, R., Worrell, J.: LTL model checking of interval markov chains. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013 (ETAPS 2013). LNCS, vol. 7795, pp. 32–46. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  3. Češka, M., Dannenberg, F., Kwiatkowska, M., Paoletti, N.: Precise parameter synthesis for stochastic biochemical systems. In: Mendes, P., Dada, J.O., Smallbone, K. (eds.) CMSB 2014. LNCS, vol. 8859, pp. 86–98. Springer, Heidelberg (2014)

    Google Scholar 

  4. Cimatti, A., Griggio, A., Mover, S., Tonetta, S.: Parameter synthesis with IC3. In: FMCAD (2013)

    Google Scholar 

  5. Cortes, C., Mansour, Y., Mohri, M.: Learning bounds for importance weighting. In: Advances in Neural Information Processing Systems (NIPS), pp. 442–450 (2010)

    Google Scholar 

  6. Daws, C.: Symbolic and parametric model checking of discrete-time Markov chains. In: Liu, Z., Araki, K. (eds.) ICTAC 2004. LNCS, vol. 3407, pp. 280–294. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Ellen, C., Gerwinn, S., Fränzle, M.: Statistical model checking for stochastic hybrid systems involving nondeterminism over continuous domains. International Journal on Software Tools for Technology Transfer 17(4), 485–504 (2015)

    Google Scholar 

  8. Fränzle, M., Herde, C., Teige, T., Ratschan, S., Schubert, T.: Efficient Solving of Large Non-linear Arithmetic Constraint Systems with Complex Boolean Structure. JSAT 1, 209–236 (2007)

    Google Scholar 

  9. Hahn, E.M., Han, T., Zhang, L.: Synthesis for PCTL in parametric Markov decision processes. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 146–161. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Hahn, E.M., Hermanns, H., Zhang, L.: Probabilistic reachability for parametric Markov models. STTT 13(1), 3–19 (2011)

    Article  Google Scholar 

  11. Han, T., Katoen, J.-P., Mereacre, A.: Approximate parameter synthesis for probabilistic time-bounded reachability. In: IEEE Real-Time Systems Symposium (RTSS), pp. 173–182. IEEE Computer Society (2008)

    Google Scholar 

  12. Herde, C., Eggers, A., Fränzle, M., Teige, T.: Analysis of hybrid systems using HySAT. In: Third International Conference on Systems, ICONS 2008, pp. 196–201. IEEE (2008)

    Google Scholar 

  13. Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 13–30 (1963)

    Google Scholar 

  14. Jansen, N., Corzilius, F., Volk, M., Wimmer, R., Ábrahám, E., Katoen, J.-P., Becker, B.: Accelerating parametric probabilistic verification. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 404–420. Springer, Heidelberg (2014)

    Google Scholar 

  15. Lanotte, R., Maggiolo-Schettini, A., Troina, A.: Parametric probabilistic transition systems for system design and analysis. Formal Aspects of Computing 19(1), 93–109 (2007)

    Article  MATH  Google Scholar 

  16. Liu, B., Kong, S., Gao, S., Zuliani, P., Clarke, E.M.: Parameter synthesis for cardiac cell hybrid models using \(\delta \)-decisions. In: Mendes, P., Dada, J.O., Smallbone, K. (eds.) CMSB 2014. LNCS, vol. 8859, pp. 99–113. Springer, Heidelberg (2014)

    Google Scholar 

  17. Liu, J., Ozay, N.: Abstraction, discretization, and robustness in temporal logic control of dynamical systems. In: Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control, pp. 293–302. ACM (2014)

    Google Scholar 

  18. Puggelli, A., Li, W., Sangiovanni-Vincentelli, A.L., Seshia, S.A.: Polynomial-time verification of PCTL properties of MDPs with convex uncertainties. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 527–542. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Sproston, J.: Decidable model checking of probabilistic hybrid automata. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 31–45. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  20. Sproston, J.: Model Checking for Probabilistic Timed and Hybrid Systems. PhD thesis, School of Computer Science, The University of Birmingham (2001)

    Google Scholar 

  21. Tokdar, S.T., Kass, R.E.: Importance sampling: a review. Wiley Interdisciplinary Reviews: Computational Statistics 2(1), 54–60 (2010)

    Article  Google Scholar 

  22. Vapnik, V.N.: Statistical learning theory, vol. 1. Wiley, New York (1998)

    MATH  Google Scholar 

  23. Wimmer, R., Derisavi, S., Hermanns, H.: Symbolic partition refinement with dynamic balancing of time and space. In: Rubino, G. (ed.) Quantitative Evaluation of Systems (QEST), pp. 65–74. IEEE Computer Science Press (2008)

    Google Scholar 

  24. Younes, H.L.S., Kwiatkowska, M., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking. International Journal on Software Tools for Technology Transfer (STTT) 8(3), 216–228 (2006)

    Article  Google Scholar 

  25. Zhang, Y., Sankaranarayanan, S., Somenzi, F.: Statistically sound verification and optimization for complex systems. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 411–427. Springer, Heidelberg (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing Science, Carl von Ossietzky University, Oldenburg, Germany

    Martin Fränzle & Paul Kröger

  2. OFFIS Institute for Information Technology, Oldenburg, Germany

    Martin Fränzle & Sebastian Gerwinn

  3. Department of Computer Science, Oxford University, Oxford, UK

    Alessandro Abate

  4. Department of Computer Science, RWTH Aachen University, Aachen, Germany

    Joost-Pieter Katoen

Authors
  1. Martin Fränzle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian Gerwinn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paul Kröger
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alessandro Abate
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Joost-Pieter Katoen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sebastian Gerwinn .

Editor information

Editors and Affiliations

  1. University of Colorado, Boulder, Colorado, USA

    Sriram Sankaranarayanan

  2. University of Florence, Florence, Italy

    Enrico Vicario

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Fränzle, M., Gerwinn, S., Kröger, P., Abate, A., Katoen, JP. (2015). Multi-objective Parameter Synthesis in Probabilistic Hybrid Systems. In: Sankaranarayanan, S., Vicario, E. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2015. Lecture Notes in Computer Science(), vol 9268. Springer, Cham. https://doi.org/10.1007/978-3-319-22975-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22975-1_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22974-4

  • Online ISBN: 978-3-319-22975-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation