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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
http://www.mathworks.com/products.
- 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
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)
Nerode, A., Kohn, W.: Models for hybrid systems: automata, topologies, controllability, observability. In: [23], pp. 317–356 (1993)
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
Davis, M.: Markov Models and Optimization. Chapman & Hall, London (1993)
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
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)
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
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)
Kowalewski, S., et al.: Hybrid Automata, pp. 57–86. Cambridge University Press, Cambridge (2009)
Maschler, M., Solan, E., Zamir, S.: Game Theory. Cambridge University Press, Cambridge (2013)
Barber, D.: Bayesian Reasoning and Machine Learning. Cambride University Press, Cambridge (2012)
Langseth, H., Nielsen, T.D., Rum, R., Salmern, A.: Inference in hybrid Bayesian networks. Reliab. Eng. Syst. Saf. 94(10), 1499–1509 (2009)
Mahler, R.P.S.: Multitarget bayes filtering via first-order multitarget moments. IEEE Trans. Aerosp. Electron. Syst. 39(4), 1152–1178 (2003). October
Elfes, A.: Using occupancy grids for mobile robot perception and navigation. Computer 22(6), 46–57 (1989). June
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/
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
Sherlock, C., Golightly, A., Gillespie, C.S.: Bayesian inference for hybrid discrete-continuous stochastic kinetic models. Inverse Probl. 30(11), 114005 (2014). November
Murphy, K.P.: Switching kalman filters. Technical report (1998)
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)
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
Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans. ASME-J. Basic Eng. 82(Series D), 35–45 (1960)
Thrun, S.: Probabilistic robotics. Commun. ACM 45(3), 52–57 (2002). March
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-01461-2_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01460-5
Online ISBN: 978-3-030-01461-2
eBook Packages: Computer ScienceComputer Science (R0)