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Symposium on Real-Time and Hybrid Systems pp 165–185Cite as

The Demon, the Gambler, and the Engineer

Reconciling Hybrid-System Theory with Metrology

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11180))

Abstract

Hybrid discrete-continuous system dynamics arises when discrete actions, e.g. by a decision algorithm, meet continuous behaviour, e.g. due to physical processes and continuous control. Various flavours of hybrid automata have been suggested as a means to formally analyse such dynamical systems, among them deterministic automata models facilitating reasoning about their normative behaviour, nondeterministic automata under a demonic interpretation supporting worst-case analysis, and stochastic variants enabling quantitative verification. In this article, we demonstrate that all these variants provide imprecise, in the sense of either overly pessimistic or overly optimistic, verdicts for engineered systems operating under uncertain observation of their environment due to, e.g., measurement error. We argue that even the most elaborate models of hybrid automata currently available ignore wisdom from metrology and game theory concerning environmental state estimation to be pursued by a rational player, which a control system obviously ought to constitute. We consequently suggest a revised formal model, called Bayesian hybrid automata, that is able to represent state tracking and estimation in hybrid systems and thereby enhances precision of verdicts obtained from the model.

For their work on this subject, the authors received funding from Deutsche Forschungsgemeinschaft under grant number DFG GRK 1765, covering the Research Training Group SCARE: System Correctness under Adverse Conditions.

M. Fränzle dedicates this article to Zhou Chaochen in grateful remembrance of Zhou introducing him to the field of formal models for hybrid-system dynamics a quarter of a century ago.

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Notes

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  2. 2.

    An accurate verdict for liveness could actually be achieved if fairness conditions were part of the automaton model, but hybrid automata tend to omit such.

References

  1. Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.: Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: [23], pp. 209–229 (1993)

    Chapter  Google Scholar 

  2. Nerode, A., Kohn, W.: Models for hybrid systems: automata, topologies, controllability, observability. In: [23], pp. 317–356 (1993)

    Chapter  Google Scholar 

  3. Sproston, J.: Decidable model checking of probabilistic hybrid automata. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 31–45. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45352-0_5

    Chapter  Google Scholar 

  4. Davis, M.: Markov Models and Optimization. Chapman & Hall, London (1993)

    Book  Google Scholar 

  5. Fränzle, M., Hermanns, H., Teige, T.: Stochastic satisfiability modulo theory: a novel technique for the analysis of probabilistic hybrid systems. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 172–186. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78929-1_13

    Chapter  MATH  Google Scholar 

  6. Fränzle, M., Hahn, E.M., Hermanns, H., Wolovick, N., Zhang, L.: Measurability and safety verification for stochastic hybrid systems. In Caccamo, M., Frazzoli, E., Grosu, R. (eds.) Proceedings of the 14th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2011, 12–14 April 2011, pp. 43–52. ACM, Chicago (2011)

    Google Scholar 

  7. Hu, J., Lygeros, J., Sastry, S.: Towards a theory of stochastic hybrid systems. In: Lynch, N., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 160–173. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-46430-1_16

    Chapter  MATH  Google Scholar 

  8. Bujorianu, L., Lygeros, J.: Toward a general theory of stochastic hybrid systems. Stochastic Hybrid Systems: Theory and Safety Critical Applications. LNCIS, vol. 337, pp. 3–30. Springer, Berlin (2006)

    Google Scholar 

  9. Kowalewski, S., et al.: Hybrid Automata, pp. 57–86. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  10. Maschler, M., Solan, E., Zamir, S.: Game Theory. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  11. Barber, D.: Bayesian Reasoning and Machine Learning. Cambride University Press, Cambridge (2012)

    Google Scholar 

  12. Langseth, H., Nielsen, T.D., Rum, R., Salmern, A.: Inference in hybrid Bayesian networks. Reliab. Eng. Syst. Saf. 94(10), 1499–1509 (2009)

    Article  Google Scholar 

  13. Mahler, R.P.S.: Multitarget bayes filtering via first-order multitarget moments. IEEE Trans. Aerosp. Electron. Syst. 39(4), 1152–1178 (2003). October

    Article  Google Scholar 

  14. Elfes, A.: Using occupancy grids for mobile robot perception and navigation. Computer 22(6), 46–57 (1989). June

    Article  Google Scholar 

  15. Coué, C., Pradalier, C., Laugier, C., Fraichard, T., Bessiere, P.: Bayesian occupancy filtering for multitarget tracking: an automotive application. Int. J. Robot. Res. 25(1), 19–30 (2006). voir basilic : http://emotion.inrialpes.fr/bibemotion/2006/CPLFB06/

    Article  Google Scholar 

  16. Combastel, C.: Merging kalman filtering and zonotopic state bounding for robust fault detection under noisy environment. IFAC-PapersOnLine 48(21) (2015) 289–295; In: 9th IFAC Symposium on Fault Detection, Supervision andSafety for Technical Processes SAFEPROCESS 2015

    Article  Google Scholar 

  17. Sherlock, C., Golightly, A., Gillespie, C.S.: Bayesian inference for hybrid discrete-continuous stochastic kinetic models. Inverse Probl. 30(11), 114005 (2014). November

    Article  MathSciNet  Google Scholar 

  18. Murphy, K.P.: Switching kalman filters. Technical report (1998)

    Google Scholar 

  19. Ding, J., Abate, A., Tomlin, C.: Optimal control of partially observable discrete time stochastic hybrid systems for safety specifications. In: 2013 American Control Conference, pp. 6231–6236 (2013)

    Google Scholar 

  20. Donzé, A., Maler, O.: Robust satisfaction of temporal logic over real-valued signals. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 92–106. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15297-9_9

    Chapter  MATH  Google Scholar 

  21. Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans. ASME-J. Basic Eng. 82(Series D), 35–45 (1960)

    Article  Google Scholar 

  22. Thrun, S.: Probabilistic robotics. Commun. ACM 45(3), 52–57 (2002). March

    Article  Google Scholar 

  23. Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds.): HS 1991-1992. LNCS, vol. 736. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57318-6

    Book  Google Scholar 

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Authors and Affiliations

  1. Department of Computing Science, Carl von Ossietzky Universität Oldenburg, 26111, Oldenburg, Germany

    Martin Fränzle & Paul Kröger

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  1. Martin Fränzle
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  2. Paul Kröger
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Correspondence to Paul Kröger .

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Editors and Affiliations

  1. Newcastle University, Newcastle, UK

    Cliff Jones

  2. National University of Defense Technology, Changsha, China

    Ji Wang

  3. Institute of Software, CAS, Beijing, China

    Naijun Zhan

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Fränzle, M., Kröger, P. (2018). The Demon, the Gambler, and the Engineer. In: Jones, C., Wang, J., Zhan, N. (eds) Symposium on Real-Time and Hybrid Systems. Lecture Notes in Computer Science(), vol 11180. Springer, Cham. https://doi.org/10.1007/978-3-030-01461-2_9

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  • DOI: https://doi.org/10.1007/978-3-030-01461-2_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01460-5

  • Online ISBN: 978-3-030-01461-2

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