Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter Oldenbourg October 13, 2021

Bayesian hybrid automata: Reconciling formal methods with metrology

  • Paul Kröger

    Paul Kröger is a Ph. D. student within the Hybrid Systems group at the Department of Computing Science of the Carl von Ossietzky Universität Oldenburg (CvO). He studied Computer Science at CvO and completed his M. Sc. in 2017. His research focusses on modelling and verification of cyber-physical systems.

    EMAIL logo
    and Martin Fränzle

    Prof. Dr. Martin Fränzle Martin Fränzle has been Professor for Hybrid Systems within the Department of Computing Science at the University of Oldenburg since 2004 and the university’s Vice President for Research, Transfer, and Digitalization since 2020. He holds a diploma and a doctoral degree in Computer Science from the University of Kiel and was an associate professor and later a Velux visiting professor at the Technical University of Denmark. Further visiting professorships and extended research stays led him to Freiburg and Saarbrücken (both Germany), Copenhagen (Denmark), Tallinn (Estonia), Grenoble (France), Oxford (UK), and the Chinese Academy of Sciences. Fränzle’s research focuses on the mathematical modelling as well as the verification and synthesis of secure and reliable cyber-physical systems, i. e., the merging of physical objects with information technology into “smart” infrastructures such as autonomous vehicles, production facilities, or supply networks. His research interests thereby span from theoretical foundations to applications and industrial transfer, the latter often pursued within the associated research institute OFFIS e. V., where he is long-standing member of the executive board of the R&D division Transportation.

Abstract

Hybrid system dynamics arises when discrete actions meet continuous behaviour due to physical processes and continuous control. A natural domain of such systems are emerging smart technologies which add elements of intelligence, co-operation, and adaptivity to physical entities. Various flavours of hybrid automata have been suggested as a means to formally analyse dynamics of such systems. In this article, we present our current work on a revised formal model that is able to represent state tracking and estimation in hybrid systems and thereby enhancing precision of verification verdicts.

ACM CCS:

Award Identifier / Grant number: GRK 1765

Funding statement: This research was supported by Deutsche Forschungsgemeinschaft through the grants DFG GRK 1765 “System Correctness under Adverse Conditions” and FR 2715/4-1 “Integrated Socio-technical Models for Conflict Resolution and Causal Reasoning”.

About the authors

Paul Kröger

Paul Kröger is a Ph. D. student within the Hybrid Systems group at the Department of Computing Science of the Carl von Ossietzky Universität Oldenburg (CvO). He studied Computer Science at CvO and completed his M. Sc. in 2017. His research focusses on modelling and verification of cyber-physical systems.

Prof. Dr. Martin Fränzle

Prof. Dr. Martin Fränzle Martin Fränzle has been Professor for Hybrid Systems within the Department of Computing Science at the University of Oldenburg since 2004 and the university’s Vice President for Research, Transfer, and Digitalization since 2020. He holds a diploma and a doctoral degree in Computer Science from the University of Kiel and was an associate professor and later a Velux visiting professor at the Technical University of Denmark. Further visiting professorships and extended research stays led him to Freiburg and Saarbrücken (both Germany), Copenhagen (Denmark), Tallinn (Estonia), Grenoble (France), Oxford (UK), and the Chinese Academy of Sciences. Fränzle’s research focuses on the mathematical modelling as well as the verification and synthesis of secure and reliable cyber-physical systems, i. e., the merging of physical objects with information technology into “smart” infrastructures such as autonomous vehicles, production facilities, or supply networks. His research interests thereby span from theoretical foundations to applications and industrial transfer, the latter often pursued within the associated research institute OFFIS e. V., where he is long-standing member of the executive board of the R&D division Transportation.

References

1. R. Alur, C. Courcoubetis, T. A. Henzinger, and P.-H. Ho. Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In Hybrid Systems, volume 736 of LNCS, pages 209–229. Springer Berlin Heidelberg, 1993.10.1007/3-540-57318-6_30Search in Google Scholar

2. K. Berntorp and S. Di Cairano. Particle filtering for automotive: A survey. In 22th International Conference on Information Fusion, pages 1–8, July 2019.10.23919/FUSION43075.2019.9011201Search in Google Scholar

3. C. Combastel. Merging kalman filtering and zonotopic state bounding for robust fault detection under noisy environment. IFAC-PapersOnLine, 48(21):289–295, 2015. SAFEPROCESS 2015.10.1016/j.ifacol.2015.09.542Search in Google Scholar

4. C. Coué, C. Pradalier, C. Laugier, T. Fraichard, and P. Bessiere. Bayesian Occupancy Filtering for Multitarget Tracking: an Automotive Application. International Journal of Robotics Research, 25(1):19–30, Jan. 2006.10.1177/0278364906061158Search in Google Scholar

5. A. Donzé and O. Maler. Robust satisfaction of temporal logic over real-valued signals. In Formal Modeling and Analysis of Timed Systems, pages 92–106. Springer Berlin Heidelberg, Berlin, Heidelberg, 2010.10.1007/978-3-642-15297-9_9Search in Google Scholar

6. A. Elfes. Using occupancy grids for mobile robot perception and navigation. Computer, 22(6):46–57, 1989.10.1109/2.30720Search in Google Scholar

7. M. Fränzle, E. M. H. Hahn, H. Hermanns, N. Wolovick, and L. Zhang. Measurability and safety verification for stochastic hybrid systems. In Hybrid Systems: Computation and Control, Jan. 2011.10.1145/1967701.1967710Search in Google Scholar

8. M. Fränzle, H. Hermanns, and T. Teige. Stochastic satisfiability modulo theory: A novel technique for the analysis of probabilistic hybrid systems. In Hybrid Systems: Computation and Control, pages 172–186. Springer Berlin Heidelberg, Berlin, Heidelberg, 2008.10.1007/978-3-540-78929-1_13Search in Google Scholar

9. M. Fränzle and P. Kröger. The demon, the gambler, and the engineer – reconciling hybrid-system theory with metrology. In Symposium on Real-Time and Hybrid Systems, volume 11180 of Theoretical Computer Science and General Issues, pages 165–185. Springer International Publishing, Cham, 2018.10.1007/978-3-030-01461-2_9Search in Google Scholar

10. M. Fränzle and P. Kröger. Guess what I’m doing! In Leveraging Applications of Formal Methods, Verification and Validation: Applications, pages 255–272. Springer International Publishing, Cham, 2020.10.1007/978-3-030-61467-6_17Search in Google Scholar

11. A. Gambier. Multivariable adaptive state-space control: A survey. In 2004 5th Asian Control Conference (IEEE Cat. No. 04EX904), volume 1, pages 185–191, July 2004.Search in Google Scholar

12. J. Hu, J. Lygeros, and S. Sastry. Towards a Theory of Stochastic Hybrid Systems, pages 160–173. Springer Berlin Heidelberg, Berlin, Heidelberg, 2000.10.1007/3-540-46430-1_16Search in Google Scholar

13. R. E. Kalman. A new approach to linear filtering and prediction problems. Transactions of the ASME–Journal of Basic Engineering, 82(Series D):35–45, 1960.10.1115/1.3662552Search in Google Scholar

14. S. Kowalewski, M. Garavello, H. Guéguen, G. Herberich, R. Langerak, B. Piccoli, J. W. Polderman, and C. Weise. Hybrid automata, pages 57–86. Cambridge University Press, 2009.10.1017/CBO9780511807930.004Search in Google Scholar

15. P. Kröger and M. Fränzle. Bayesian hybrid automata: A formal model of justified belief in interacting hybrid systems subject to imprecise observation. Submitted to LITES Special Issue on Distributed Hybrid Systems. 2021.Search in Google Scholar

16. E. Lavretsky. Robust and Adaptive Control Methods for Aerial Vehicles, pages 675–710. Springer Netherlands, Dordrecht, 2015.10.1007/978-90-481-9707-1_50Search in Google Scholar

17. M. Maschler, E. Solan, and S. Zamir. Game Theory. Cambridge University Press, 2013.10.1017/CBO9780511794216Search in Google Scholar

18. K. S. Narendra and Z. Han. Adaptive control using collective information obtained from multiple models. IFAC Proceedings Volumes, 44(1):362–367, 2011. 18th IFAC World Congress.10.3182/20110828-6-IT-1002.02237Search in Google Scholar

19. A. Nerode and W. Kohn. Models for hybrid systems: Automata, topologies, controllability, observability. In Hybrid Systems, pages 317–356. Springer Berlin Heidelberg, Berlin, Heidelberg, 1993.10.1007/3-540-57318-6_35Search in Google Scholar

20. S. Särkkä. Bayesian Filtering and Smoothing. Cambridge University Press, New York, NY, USA, 2013.10.1017/CBO9781139344203Search in Google Scholar

21. C. Sherlock, A. Golightly, and C. S. Gillespie. Bayesian inference for hybrid discrete-continuous stochastic kinetic models. Inverse Problems, 30(11):114005, Nov. 2014.10.1088/0266-5611/30/11/114005Search in Google Scholar

22. J. Sproston. Decidable Model Checking of Probabilistic Hybrid Automata, pages 31–45. Springer Berlin Heidelberg, Berlin, Heidelberg, 2000.10.1007/3-540-45352-0_5Search in Google Scholar

Received: 2021-03-07
Revised: 2021-08-13
Accepted: 2021-08-24
Published Online: 2021-10-13
Published in Print: 2021-11-25

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 27.4.2024 from https://www.degruyter.com/document/doi/10.1515/itit-2021-0008/html
Scroll to top button