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Preliminary Verification of Liveness in a Control Part of Cyber-Physical Systems Modeled by a Petri Net

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Technological Innovation for Connected Cyber Physical Spaces (DoCEIS 2023)

Abstract

This paper proposes a novel approach for the liveness verification of a Petri net-based cyber-physical system (CPS). The idea is based on the reduction of the initial Petri net and further analysis of its structure in order to identify the sequences of places and transitions that may affect the liveness of the system. In particular, the technique searches for the sequences in the Petri net in order to determine whether the system may not be live, or, (in certain cases) it is definitely not live. The proposed method is mainly aimed at accelerating the process of initial verification of the control part of CPS. The main benefit of the presented technique is its polynomial computational complexity (the method runs in polynomial time). Therefore, the technique permits rapid checking of the system. Although this method is oriented toward CPSs, it can also be applied to other Petri net-based systems where liveness is especially important (e.g., concurrent control systems). The proposed technique was examined experimentally with a set of 242 benchmarks.

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References

  1. Ryalat, M., ElMoaqet, H., AlFaouri, M.: Design of a smart factory based on cyber-physical systems and Internet of Things towards Industry 4.0. Appl. Sci. 13, 2156 (2023). https://doi.org/10.3390/app13042156

  2. Lee, E.A., Seshia, S.A.: Introduction to Embedded Systems: A Cyber-Physical Systems Approach. MIT Press, Cambridge (2017)

    MATH  Google Scholar 

  3. Shih, C.-S., Chou, J.-J., Reijers, N., Kuo, T.-W.: Designing CPS/IoT applications for smart buildings and cities. IET Cyber-Phys. Syst. Theory Appl. 1, 3–12 (2016). https://doi.org/10.1049/iet-cps.2016.0025

    Article  Google Scholar 

  4. 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, 74 (2018). https://doi.org/10.1007/s10916-018-0921-x

    Article  Google Scholar 

  5. Wiśniewski, R., Bazydło, G., Szcześniak, P.: Low-cost FPGA hardware implementation of matrix converter switch control. IEEE Trans. Circ. Syst. II Express Briefs 66, 1177–1181 (2019). https://doi.org/10.1109/TCSII.2018.2875589

  6. Patalas-Maliszewska, J., Posdzich, M., Skrzypek, K.: Modelling Information for the burnishing process in a cyber–physical production system. Int. J. Appl. Math. Comput. Sci. 32, 345–354 (2022). https://doi.org/10.34768/amcs-2022-0025

  7. Guo, Y., Hu, X., Hu, B., Cheng, J., Zhou, M., Kwok, R.Y.K.: Mobile cyber physical systems: current challenges and future networking applications. IEEE Access 6, 12360–12368 (2018). https://doi.org/10.1109/ACCESS.2017.2782881

    Article  Google Scholar 

  8. Lee, E.A.: Cyber physical systems: design challenges. In: 2008 11th IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC), pp. 363–369 (2008). https://doi.org/10.1109/ISORC.2008.25

  9. Wiśniewski, R., Wojnakowski, M., Li, Z.: Design and verification of Petri-net-based cyber-physical systems oriented toward implementation in field-programmable gate arrays—a case study example. Energies 16, 67 (2023). https://doi.org/10.3390/en16010067

    Article  Google Scholar 

  10. Murata, T.: Petri nets: properties, analysis and applications. Proc. IEEE 77, 541–580 (1989). https://doi.org/10.1109/5.24143

    Article  Google Scholar 

  11. Liu, Z., Hu, L., Hu, W., Tan, J.: Petri nets-based modeling solution for cyber-physical product control considering scheduling, deployment, and data-driven monitoring. IEEE Trans. Syst. Man Cybern. Syst. 53, 990–1002 (2023). https://doi.org/10.1109/TSMC.2022.3170489

    Article  Google Scholar 

  12. Wojnakowski, M., Wiśniewski, R., Bazydło, G., Popławski, M.: Analysis of safeness in a Petri net-based specification of the control part of cyber-physical systems. Int. J. Appl. Math. Comput. Sci. 31, 647–657 (2021). https://doi.org/10.34768/amcs-2021-0045

  13. Girault, C., Valk, R.: Petri Nets for Systems Engineering. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-662-05324-9

    Book  MATH  Google Scholar 

  14. Wiśniewski, R., Bazydło, G., Gomes, L., Costa, A., Wojnakowski, M.: Analysis and design automation of cyber-physical system with hippo and IOPT-tools. In: IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, pp. 5843–5848. IEEE Press (2019). https://doi.org/10.1109/IECON.2019.8926692

  15. Wiśniewski, R.: Prototyping of Concurrent Control Systems Implemented in FPGA Devices. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-45811-3

    Book  MATH  Google Scholar 

  16. 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, 269–281 (2018). https://doi.org/10.2478/amcs-2018-0019

    Article  MathSciNet  MATH  Google Scholar 

  17. Karatkevich, A.: Dynamic Analysis of Petri Net-Based Discrete Systems. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71560-3

    Book  MATH  Google Scholar 

  18. Best, E., Devillers, R., Koutny, M.: Petri Net Algebra. Springer, Heidelberg (2001). https://doi.org/10.1007/978-3-662-04457-5

    Book  MATH  Google Scholar 

  19. David, R., Alla, H.: Bases of petri nets. In: David, R., Alla, H. (eds.) Discrete, Continuous, and Hybrid Petri Nets, pp. 1–20. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-10669-9_1

    Chapter  Google Scholar 

  20. Wojnakowski, M., Wiśniewski, R.: 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.) DoCEIS 2021. IAICT, vol. 626, pp. 83–91. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-78288-7_8

    Chapter  Google Scholar 

  21. Silva, M., Colom, J.M., Campos, J.: Linear algebraic techniques for the analysis of Petri nets. In: Recent Advances in Mathematical Theory of Systems, Control, Networks, and Signal Processing II, Tokyo, Japan, pp. 35–42. Mita Press (1992)

    Google Scholar 

  22. Esparza, J., Silva, M.: A polynomial-time algorithm to decide liveness of bounded free choice nets. Theor. Comput. Sci. 102, 185–205 (1992). https://doi.org/10.1016/0304-3975(92)90299-U

    Article  MathSciNet  MATH  Google Scholar 

  23. Barkaoui, K., Minoux, M.: A polynomial-time graph algorithm to decide liveness of some basic classes of bounded Petri nets. In: Jensen, K. (ed.) ICATPN 1992. LNCS, vol. 616, pp. 62–75. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55676-1_4

    Chapter  Google Scholar 

  24. Guo, X., Wang, S., You, D., Li, Z., Jiang, X.: A siphon-based deadlock prevention strategy for S3PR. IEEE Access 7, 86863–86873 (2019). https://doi.org/10.1109/ACCESS.2019.2920677

    Article  Google Scholar 

  25. 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

    Article  Google Scholar 

  26. Grobelna, I., Wiśniewski, R., Grobelny, M., Wiśniewska, M.: Design and verification of real-life processes with application of Petri nets. IEEE Trans. Syst. Man Cybern. Syst. 47, 2856–2869 (2017). https://doi.org/10.1109/TSMC.2016.2531673

    Article  Google Scholar 

  27. Wojnakowski, M., Popławski, M., Wiśniewski, R., Bazydło, G.: Hippo-CPS: verification of boundedness, safeness and liveness of Petri net-based cyber-physical systems. In: Camarinha-Matos, L.M. (ed.) Technological Innovation for Digitalization and Virtualization, pp. 74–82. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-07520-9_7

    Chapter  Google Scholar 

  28. He, W., Zhang(Justin), Z., Li, W.: Information technology solutions, challenges, and suggestions for tackling the COVID-19 pandemic. Int. J. Inf. Manag. 57, 102287 (2021). https://doi.org/10.1016/j.ijinfomgt.2020.102287

  29. Foresti, R., Rossi, S., Magnani, M., Guarino Lo Bianco, C., Delmonte, N.: Smart society and artificial intelligence: big data scheduling and the global standard method applied to smart maintenance. Engineering 6, 835–846 (2020). https://doi.org/10.1016/j.eng.2019.11.014

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Acknowledgments

This work is supported by the National Science Centre, Poland, under Grant number 2019/35/B/ST6/01683.

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Correspondence to Mateusz Popławski .

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Popławski, M., Wiśniewski, R., Bazydło, G., Maliński, M. (2023). Preliminary Verification of Liveness in a Control Part of Cyber-Physical Systems Modeled by a Petri Net. In: Camarinha-Matos, L.M., Ferrada, F. (eds) Technological Innovation for Connected Cyber Physical Spaces. DoCEIS 2023. IFIP Advances in Information and Communication Technology, vol 678. Springer, Cham. https://doi.org/10.1007/978-3-031-36007-7_15

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  • DOI: https://doi.org/10.1007/978-3-031-36007-7_15

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