Abstract
We introduce feedback-control statistical system checking (FC-SSC), a new approach to statistical model checking that exploits principles of feedback-control for the analysis of cyber-physical systems (CPS). FC-SSC uses stochastic system identification to learn a CPS model, importance sampling to estimate the CPS state, and importance splitting to control the CPS so that the probability that the CPS satisfies a given property can be efficiently inferred. We illustrate the utility of FC-SSC on two example applications, each of which is simple enough to be easily understood, yet complex enough to exhibit all of FC-SCC’s features. To the best of our knowledge, FC-SSC is the first statistical system checker to efficiently estimate the probability of rare events in realistic CPS applications or in any complex probabilistic program whose model is either not available, or is infeasible to derive through static-analysis techniques.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Importance splitting has been first used in [14] to estimate the probability that neutrons would pass through certain shielding materials. The distance traveled in the shield can then be used to define a set of increasing levels \(0\,{=}\,\ell _{1}\,{<}\,\ell _{2}\,{<}\cdots {<}\,\ell _{n}{=}\,\tau \) that may be reached by the paths of neutrons, with the property that reaching a given level implies having reached all the lower levels.
References
Code repository. https://ti.tuwien.ac.at/tacas2015/
Barbara, M., Frédéric, D., Gerhard, R., Alain, L., Frans, J., Thierry, P. (eds.): Parallel Computing: From Multicores and GPU’s to Petascale. Advances in Parallel Computing, vol. 19. IOS Press, Amsterdam (2010). Proceedings of the Conference ParCo 2009, 1–4, September 2009, Lyon, France
Bartocci, E., Grosu, R., Karmarkar, A., Smolka, S.A., Stoller, S.D., Zadok, E., Seyster, J.: Adaptive runtime verification. In: Qadeer, S., Tasiran, S. (eds.) RV 2012. LNCS, vol. 7687, pp. 168–182. Springer, Heidelberg (2013). doi:10.1007/978-3-642-35632-2_18
Broy, M., Geisberger, E.: Cyber-physical Systems, Driving Force for Innovation in Mobility, Health, Energy and Production. The National Academy Of Science and Engineering, Acatech (2012)
Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)
Clarke, E.M., Zuliani, P.: Statistical model checking for cyber-physical systems. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 1–12. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24372-1_1
Doucet, A., de Freitas, N., Gordon, N.: Sequential Monte Carlo Methods in Practice. Springer, New York (2001)
Duflot, M., Fribourg, L., Picaronny, C.: Randomized dining philosophers without fairness assumption. Distrib. Comput. 17(1), 65–76 (2004)
Glasserman, P., Heidelberger, P., Shahabuddin, P., Zajic, T.: Multilevel Splitting for Estimating Rare Event Probabilities. Oper. Res. 47(4), 585–600 (1999)
Grosu, R., Smolka, S.A.: Monte Carlo model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 271–286. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31980-1_18
Jegourel, C., Legay, A., Sedwards, S.: Cross-entropy optimisation of importance sampling parameters for statistical model checking. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 327–342. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31424-7_26
Jegourel, C., Legay, A., Sedwards, S.: Importance splitting for statistical model checking rare properties. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 576–591. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39799-8_38
Jegourel, C., Legay, A., Sedwards, S.: An effective heuristic for adaptive importance splitting in statistical model checking. In: Margaria, T., Steffen, B. (eds.) ISoLA 2014. LNCS, vol. 8803, pp. 143–159. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45231-8_11
Kahn, H., Harris, T.E.: Estimation of particle transmission by random sampling. In: Applied Mathematics, vol. 5 of series 12. National Bureau of Standards (1951)
Kalajdzic, K., Bartocci, E., Smolka, S.A., Stoller, S.D., Grosu, R.: Runtime verification with particle filtering. In: Legay, A., Bensalem, S. (eds.) RV 2013. LNCS, vol. 8174, pp. 149–166. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40787-1_9
Kanungo, T.: UMDHMM tool. http://www.kanungo.com/software/software.html
Rabiner, L.: A tutorial on hidden Markov models, selected applications in speech recognition. Proc. IEEE 77(2), 257–286 (1989)
Roweis, S., Ghahramani, Z.: A unifying review of linear gaussian models. Neural Comput. 11(2), 305–345 (1999)
Russell, S., Norvig, P., Intelligence, A.: A Modern Approach, 3rd edn. Prentice-Hall, Upper Saddle River (2010)
Stoller, S.D., Bartocci, E., Seyster, J., Grosu, R., Havelund, K., Smolka, S.A., Zadok, E.: Runtime verification with state estimation. In: Khurshid, S., Sen, K. (eds.) RV 2011. LNCS, vol. 7186, pp. 193–207. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29860-8_15
Verma, V., Gordon, G., Simmons, R., Thrun, S.: Real-time fault diagnosis [robot fault diagnosis]. IEEE Robot. Autom. Mag. 11(2), 56–66 (2004)
Younes, H., Kwiatkowska, M., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking. STTT 8(3), 216–228 (2006)
Zuliani, P., Baier, C., Clarke, E.: Rare-event verification for stochastic hybrid systems. In: Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2012, pp. 217–226. ACM (2012)
Acknowledgements
This work was partially supported by the Doctoral Program Logical Methods in Computer Science funded by the Austrian FWF, and the Austrian National Research Network (nr. S 11405-N23 and S 11412-N23) SHiNE funded by the Austrian Science Fund (FWF).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Kalajdzic, K. et al. (2016). Feedback Control for Statistical Model Checking of Cyber-Physical Systems. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation: Foundational Techniques. ISoLA 2016. Lecture Notes in Computer Science(), vol 9952. Springer, Cham. https://doi.org/10.1007/978-3-319-47166-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-47166-2_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47165-5
Online ISBN: 978-3-319-47166-2
eBook Packages: Computer ScienceComputer Science (R0)