Statistical Model Checking for Distributed Probabilistic-Control Hybrid Automata with Smart Grid Applications

  • João Martins
  • André Platzer
  • João Leite
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6991)

Abstract

The power industry is currently moving towards a more dynamical, intelligent power grid. This Smart Grid is still in its infancy and a formal evaluation of the expensive technologies and ideas on the table is necessary before committing to a full investment. In this paper, we argue that a good model for the Smart Grid must match its basic properties: it must be hybrid (both evolve over time, and perform control/computation), distributed (multiple concurrently executing entities), and allow for asynchronous communication and stochastic behaviour (to accurately model real-world power consumption). We propose Distributed Probabilistic-Control Hybrid Automata (Dpcha) as a model for this purpose, and extend Bounded LTL to Quantified Bounded LTL in order to adapt and apply existing statistical model-checking techniques. We provide an implementation of a framework for developing and verifying DPCHAs. Finally, we conduct a case study for Smart Grid communications analysis.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.H.: Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, Springer, Heidelberg (1993)CrossRefGoogle Scholar
  2. 2.
    Demongodin, I., Koussoulas, N.: Differential Petri nets: representing continuous systems in a discrete-event world. IEEE Transactions on Automatic Control 43(4), 573–579 (1998)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Henzinger, T.A.: The theory of hybrid automata. In: LICS (1996)Google Scholar
  4. 4.
    Legay, A., Delahaye, B., Bensalem, S.: Statistical model checking: An overview. In: Barringer, H., Falcone, Y., Finkbeiner, B., Havelund, K., Lee, I., Pace, G., Roşu, G., Sokolsky, O., Tillmann, N. (eds.) RV 2010. LNCS, vol. 6418, pp. 122–135. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Lynch, N.A.: Input/Output automata: Basic, timed, hybrid, probabilistic, dynamic,.. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 187–188. Springer, Heidelberg (2003)Google Scholar
  6. 6.
    Lynch, N.A., Segala, R., Vaandrager, F.W., Weinberg, H.B.: Hybrid I/O automata. In: Alur, R., Sontag, E.D., Henzinger, T.A. (eds.) HS 1995. LNCS, vol. 1066, Springer, Heidelberg (1996)Google Scholar
  7. 7.
    Martins, J., Platzer, A., Leite, J.: Statistical model checking for distributed probabilistic-control hybrid automata in the smart grid. Tech. Rep. CMU-CS-11-119, Computer Science Department, Carnegie Mellon University (2011)Google Scholar
  8. 8.
    Meseguer, J., Sharykin, R.: Specification and analysis of distributed object-based stochastic hybrid systems. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 460–475. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Platzer, A.: Differential dynamic logic for hybrid systems. J. Autom. Reas. 41(2), 143–189 (2008)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Platzer, A.: Quantified differential dynamic logic for distributed hybrid systems. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 469–483. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Platzer, A.: Stochastic differential dynamic logic for stochastic hybrid programs. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 431–445. Springer, Heidelberg (2011)Google Scholar
  12. 12.
    Trivedi, K.S., Kulkarni, V.G.: FSPNs: Fluid stochastic Petri nets. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 24–31. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  13. 13.
    Yahav, E., Reps, T., Sagiv, M.: LTL model checking for systems with unbounded number of dynamically created threads and objects. Tech. Rep. TR-1424, Computer Sciences Department, University of Wisconsin (2001)Google Scholar
  14. 14.
    Younes, H.L.S., Simmons, R.G.: Statistical probabilistic model checking with a focus on time-bounded properties. Inf. Comput. 204(9), 1368–1409 (2006)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Zuliani, P., Platzer, A., Clarke, E.M.: Bayesian statistical model checking with application to Simulink/Stateflow verification. In: Johansson, K.H., Yi, W. (eds.) HSCC, pp. 243–252. ACM, New York (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • João Martins
    • 1
    • 2
  • André Platzer
    • 1
  • João Leite
    • 2
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA
  2. 2.CENTRIA and Departamento de InformáticaFCT, Universidade Nova de LisboaPortugal

Personalised recommendations