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.
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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.
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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).
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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
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