Abstract
A method of analysis of a control part of the cyber-physical system described by a Petri net is presented in the paper. In particular, boundedness of the system is examined. Contrary to other well-known techniques, the proposed idea does not require obtaining of all place invariants, nor computation of all reachable states in the net. Therefore, it is possible to check the boundedness of a net in a more effective and efficient way, compared to the traditional, well-known methods. Furthermore, the proposed algorithm has been examined experimentally with a set of 243 benchmarks (Petri nets). The research results show the high efficiency of the proposed method, since a solution was found even for such nets where popular techniques were not able to analyse boundedness of the system. Finally, the presented idea is illustrated by a case-study real-life example.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Girault, C., Valk, R.: Petri Nets for Systems Engineering: A Guide to Modeling, Verification, and Applications. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-662-05324-9
Karatkevich, A.: Dynamic Analysis of Petri Net-Based Discrete Systems. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71560-3
Zhou, M., Wu, N.: System Modeling and Control with Resource-Oriented Petri Nets, 1st edn. CRC Press, Boca Raton (2009)
Murata, T.: Petri nets: properties, analysis and applications. Proc. IEEE 77(4), 541–580 (1989). https://doi.org/10.1109/5.24143
Wiśniewski, R.: Prototyping of Concurrent Control Systems Implemented in FPGA Devices. Springer, Switzerland (2017). https://doi.org/10.1007/978-3-319-45811-3
Wisniewski, R., Wisniewska, M., Jarnut, M.: C-exact hypergraphs in concurrency and sequentiality analyses of cyber-physical systems specified by safe Petri nets. IEEE Access 7, 13510–13522 (2019). https://doi.org/10.1109/access.2019.2893284
Yu, Z., Zhou, L., Ma, Z., El-Meligy, M.A.: Trustworthiness modeling and analysis of cyber-physical manufacturing systems. IEEE Access 5, 26076–26085 (2017)
Grobelna, I., Wiśniewski, R., Wojnakowski, M.: Specification of cyber-physical systems with the application of interpreted nets. In: Proceedings of the IECON’19 - 45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, pp. 5887–5891 (2019)
Wiśniewski, R., Bazydło, G., Szcześniak, P., Wojnakowski, M.: Petri net-based specification of cyber-physical systems oriented to control direct matrix converters with space vector modulation. IEEE Access 7, 23407–23420 (2019). https://doi.org/10.1109/access.2019.2899316
Lee, E.A.: Cyber physical systems: design challenges. In: 2008 11th IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC), May 2008, pp. 363–369 (2008). https://doi.org/10.1109/isorc.2008.25
Lee, E.A., Seshia, S.A.: Introduction to Embedded Systems: A Cyber-Physical Systems Approach, 2nd edn. The MIT Press, Cambridge (2016)
Dey, N., Ashour, A.S., Shi, F., Fong, S.J., Tavares, J.M.R.S.: Medical cyber-physical systems: a survey. J. Med. Syst. 42(4), 74 (2018). https://doi.org/10.1007/s10916-018-0921-x
Jia, D., Lu, K., Wang, J., Zhang, X., Shen, X.: A Survey on platoon-based vehicular cyber-physical systems. IEEE Commun. Surv. Tutor. 18(1), 263–284 (2016). https://doi.org/10.1109/comst.2015.2410831
Wiśniewski, R., Bazydło, G., Szcześniak, P.: Low-cost FPGA hardware implementation of matrix converter switch control. IEEE Trans. Circuits Syst. II Express Briefs 66(7), 1177–1181 (2019). https://doi.org/10.1109/tcsii.2018.2875589
Wiśniewski, R., Karatkevich, A., Adamski, M., Costa, A., Gomes, L.: Prototyping of concurrent control systems with application of Petri nets and comparability graphs. IEEE Trans. Control Syst. Technol. 26(2), 575–586 (2018). https://doi.org/10.1109/tcst.2017.2692204
Clempner, J.: An analytical method for well-formed workflow/Petri net verification of classical soundness. Int. J. Appl. Math. Comput. Sci. 24(4), 931–939 (2014). https://doi.org/10.2478/amcs-2014-0068
Li, B., Khlif-Bouassida, M., Toguyéni, A.: On–the–fly diagnosability analysis of bounded and unbounded labeled Petri nets using verifier nets. Int. J. Appl. Math. Comput. Sci. 28(2), 269–281 (2018). https://doi.org/10.2478/amcs-2018-0019
Martínez, J., Silva, M.: A simple and fast algorithm to obtain all invariants of a generalised Petri net. In: Girault, C., Reisig, W. (eds.) Application and Theory of Petri Nets. Informatik-Fachberichte, vol. 52, pp. 301–310. Springer, Heidelberg (1982). https://doi.org/10.1007/978-3-642-68353-4_47
Reisig, W.: Nets consisting of places and transistions. In: Reisig, W. (ed.) Petri Nets. EATCS Monographs on Theoretical Computer Science, vol 4, pp. 62–76. Springer, Heidelberg (1985). https://doi.org/10.1007/978-3-642-69968-9_6
Celaya, J.R., Desrochers, A.A., Graves, R.J.: Modeling and analysis of multi-agent systems using Petri nets. In: 2007 IEEE International Conference on Systems, Man and Cybernetics, pp. 1439–1444, October 2007. https://doi.org/10.1109/icsmc.2007.4413960
Pang, G.K.H., Tang, R., Woo, S.S.: Intelligent control and supervision based on fuzzy Petri nets. In: Tzafestas, S.G. (ed.) Methods and Applications of Intelligent Control. Microprocessor-Based and Intelligent Systems Engineering, vol. 16, pp. 217–243. Springer, Dordrecht (1997). https://doi.org/10.1007/978-94-011-5498-7_8
Cang, S., Yu, H.: Overview of modelling, scheduling, planning, and control using Petri net representation and AI search. In: Advanced Design and Manufacture to Gain a Competitive Edge, London, pp. 397–406 (2008). https://doi.org/10.1007/978-1-84800-241-8_41
Edelkamp, S., Jabbar, S.: Action planning for directed model checking of Petri nets. Electron. Notes Theor. Comput. Sci. 149(2), 3–18 (2006). https://doi.org/10.1016/j.entcs.2005.07.023
Wisniewski, R., Wojnakowski, M., Stefanowicz, Ł.: Safety analysis of Petri nets based on the SM-cover computed with the linear algebra technique. In: AIP Conference Proceedings, vol. 2040, no. 1, p. 080008, November 2018. https://doi.org/10.1063/1.5079142
Wiśniewski, R., Karatkevich, A., Stefanowicz, Ł., Wojnakowski, M.: Decomposition of distributed edge systems based on the Petri nets and linear algebra technique. J. Syst. Archit. 96, 20–31 (2019). https://doi.org/10.1016/j.sysarc.2019.01.015
Zurawski, R., Zhou, M.: Petri nets and industrial applications: a tutorial. IEEE Trans. Ind. Electron. 41(6), 567–583 (1994). https://doi.org/10.1109/41.334574
Acknowledgments
This work is supported by the National Science Centre, Poland, under Grant number 2019/35/B/ST6/01683.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 IFIP International Federation for Information Processing
About this paper
Cite this paper
Wojnakowski, M., Wiśniewski, R. (2021). Verification of the Boundedness Property in a Petri Net-Based Specification of the Control Part of Cyber-Physical Systems. In: Camarinha-Matos, L.M., Ferreira, P., Brito, G. (eds) Technological Innovation for Applied AI Systems. DoCEIS 2021. IFIP Advances in Information and Communication Technology, vol 626. Springer, Cham. https://doi.org/10.1007/978-3-030-78288-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-78288-7_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-78287-0
Online ISBN: 978-3-030-78288-7
eBook Packages: Computer ScienceComputer Science (R0)