{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T02:45:29Z","timestamp":1769741129289,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T00:00:00Z","timestamp":1686700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"NATIONAL SCIENCE CENTRE, POLAND","doi-asserted-by":"publisher","award":["2019\/35\/B\/ST6\/01683"],"award-info":[{"award-number":["2019\/35\/B\/ST6\/01683"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004281","name":"NATIONAL SCIENCE CENTRE, POLAND","doi-asserted-by":"publisher","award":["UIDB\/00066\/2020\/UIDP\/00066\/2020"],"award-info":[{"award-number":["UIDB\/00066\/2020\/UIDP\/00066\/2020"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Portuguese FCT program, Center of Technology and Systems (CTS)","award":["2019\/35\/B\/ST6\/01683"],"award-info":[{"award-number":["2019\/35\/B\/ST6\/01683"]}]},{"name":"Portuguese FCT program, Center of Technology and Systems (CTS)","award":["UIDB\/00066\/2020\/UIDP\/00066\/2020"],"award-info":[{"award-number":["UIDB\/00066\/2020\/UIDP\/00066\/2020"]}]},{"name":"A. Costa","award":["2019\/35\/B\/ST6\/01683"],"award-info":[{"award-number":["2019\/35\/B\/ST6\/01683"]}]},{"name":"A. Costa","award":["UIDB\/00066\/2020\/UIDP\/00066\/2020"],"award-info":[{"award-number":["UIDB\/00066\/2020\/UIDP\/00066\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>Decomposition is one of the commonly used techniques applied in the design of Petri net-based cyber-physical systems. Such an operation permits the splitting of the initial system into sequential components that can be further implemented as an integrated or distributed system. This paper is focused on the decomposition of the modelled CPS toward its further implementation as an integrated system, namely an FPGA device. The adequate decomposition method is presented and explained in detail. Moreover, the proposed idea is explained by the real-life example of the beverage production and distribution system. The results of the experiments are presented and discussed.<\/jats:p>","DOI":"10.3390\/app13127137","type":"journal-article","created":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T02:28:56Z","timestamp":1686796136000},"page":"7137","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Decomposition of a Petri Net-Based Cyber-Physical System toward Implementation as an Integrated System within FPGA"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6829-2263","authenticated-orcid":false,"given":"Remigiusz","family":"Wi\u015bniewski","sequence":"first","affiliation":[{"name":"Institute of Control and Computation Engineering, University of Zielona G\u00f3ra, Prof. Z. Szafrana 2, 65-516 Zielona G\u00f3ra, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8147-028X","authenticated-orcid":false,"given":"Anik\u00f3","family":"Costa","sequence":"additional","affiliation":[{"name":"NOVA School of Science and Technology, Center of Technology and Systems (UNINOVA-CTS), Associated Lab of Intelligent Systems (LASI), NOVA University Lisbon, 2829-516 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9830-9262","authenticated-orcid":false,"given":"Marcin","family":"Wojnakowski","sequence":"additional","affiliation":[{"name":"Institute of Control and Computation Engineering, University of Zielona G\u00f3ra, Prof. Z. Szafrana 2, 65-516 Zielona G\u00f3ra, Poland"}]},{"given":"Maxim","family":"Mali\u0144ski","sequence":"additional","affiliation":[{"name":"University of Zielona G\u00f3ra, Prof. Z. 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Lecture Notes in Computer Science.","DOI":"10.1007\/3-540-45594-9"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/TSMCA.2003.820576","article-title":"Elementary Siphons of Petri Nets and Their Application to Deadlock Prevention in Flexible Manufacturing Systems","volume":"34","author":"Li","year":"2004","journal-title":"IEEE Trans. Syst. Man Cybern.-Part Syst. Hum."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2384","DOI":"10.1016\/j.procs.2020.09.306","article-title":"Industry 4.0 Implementation Challenges in Manufacturing Industries: An Interpretive Structural Modelling Approach","volume":"176","author":"Bakhtari","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_6","unstructured":"Reisig, W. (1985). Petri Nets: An Introduction, Springer. EATCS Monographs on Theoretical Computer Science."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Wi\u015bniewski, R. (2017). Prototyping of Concurrent Control Systems Implemented in FPGA Devices, Springer. Advances in Industrial Control.","DOI":"10.1007\/978-3-319-45811-3"},{"key":"ref_8","unstructured":"David, R., and Alla, H. (1992). Petri Nets and Grafcet: Tools for Modelling Discrete Event Systems, Prentice-Hall, Inc."},{"key":"ref_9","unstructured":"Lee, E.A., and Seshia, S.A. (2016). Introduction to Embedded Systems: A Cyber-Physical Systems Approach, The MIT Press. [2nd ed.]."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1109\/5.24143","article-title":"Petri Nets: Properties, Analysis and Applications","volume":"77","author":"Murata","year":"1989","journal-title":"Proc. IEEE"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Camarinha-Matos, L.M., Ferreira, P., and Brito, G. (2021). Technological Innovation for Applied AI Systems, Springer.","DOI":"10.1007\/978-3-030-78288-7"},{"key":"ref_12","first-page":"647","article-title":"Analysis of Safeness in a Petri Net-Based Specification of the Control Part of Cyber-Physical Systems","volume":"31","author":"Wojnakowski","year":"2021","journal-title":"Appl. Math. Comput. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Camarinha-Matos, L.M. (2022). Technological Innovation for Digitalization and Virtualization, Springer.","DOI":"10.1007\/978-3-031-07520-9"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Lee, E.A. (2008, January 5\u20137). Cyber Physical Systems: Design Challenges. Proceedings of the 2008 11th IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC), Orlando, FL, USA.","DOI":"10.1109\/ISORC.2008.25"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.mfglet.2014.12.001","article-title":"A Cyber-Physical Systems Architecture for Industry 4.0-Based Manufacturing Systems","volume":"3","author":"Lee","year":"2015","journal-title":"Manuf. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hahanov, V. (2018). Cyber Physical Computing for IoT-Driven Services, Springer.","DOI":"10.1007\/978-3-319-54825-8"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"51","DOI":"10.34768\/amcs-2022-0005","article-title":"A Feasible Schedule for Parallel Assembly Tasks in Flexible Manufacturing Systems","volume":"32","author":"Majdzik","year":"2022","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"ref_18","first-page":"345","article-title":"Modelling Information for the Burnishing Process in a Cyber\u2013Physical Production System","volume":"32","author":"Posdzich","year":"2022","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Bazyd\u0142o, G. (2023). Designing Reconfigurable Cyber-Physical Systems Using Unified Modeling Language. Energies, 16.","DOI":"10.3390\/en16031273"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1007\/s10916-018-0921-x","article-title":"Medical Cyber-Physical Systems: A Survey","volume":"42","author":"Dey","year":"2018","journal-title":"J. Med. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wojnakowski, M., Wi\u015bniewski, R., Pop\u0142awski, M., and Bazyd\u0142o, G. (2022, January 9\u201312). Analysis of Control Part of Cyber-Physical Systems Specified by Interpreted Petri Nets. Proceedings of the 2022 IEEE International Conference on Systems, Man, and Cybernetics (SMC), Prague, Czech Republic.","DOI":"10.1109\/SMC53654.2022.9945425"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wi\u015bniewski, R., Wojnakowski, M., and Li, Z. (2023). Design and Verification of Petri-Net-Based Cyber-Physical Systems Oriented toward Implementation in Field-Programmable Gate Arrays\u2014A Case Study Example. Energies, 16.","DOI":"10.3390\/en16010067"},{"key":"ref_23","first-page":"e140693","article-title":"Design Optimization of the Petri Net-Based Production Process Supported by Additive Manufacturing Technologies","volume":"70","author":"Topczak","year":"2022","journal-title":"Bull. Pol. Acad. Sci. Tech. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Patalas-Maliszewska, J., Wi\u015bniewski, R., Topczak, M., and Wojnakowski, M. (2022, January 18\u201323). Modelling of the Effectiveness of Integrating Additive Manufacturing Technologies into Petri Net-Based Manufacturing Systems. Proceedings of the 2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Padua, Italy.","DOI":"10.1109\/FUZZ-IEEE55066.2022.9882766"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wisniewski, R., Bazyd\u0142o, G., Gomes, L., Costa, A., and Wojnakowski, M. (2019, January 14\u201317). Analysis and Design Automation of Cyber-Physical System with Hippo and IOPT-Tools. Proceedings of the IECON 2019\u201445th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal.","DOI":"10.1109\/IECON.2019.8926692"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Costa, A., Gomes, L., Barros, J.P., Oliveira, J., and Reis, T. (2008, January 10\u201313). Petri Nets Tools Framework Supporting FPGA-Based Controller Implementations. Proceedings of the 2008 34th Annual Conference of IEEE Industrial Electronics, Orlando, FL, USA.","DOI":"10.1109\/IECON.2008.4758345"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kubica, M., Opara, A., and Kania, D. (2021). Technology Mapping for LUT-Based FPGA, Springer. Lecture Notes in Electrical Engineering.","DOI":"10.1007\/978-3-030-60488-2"},{"key":"ref_28","unstructured":"Zaitsev, D. (2004, January 21). Decomposition-Based Calculation of Petri Net Invariants. Proceedings of the Workshop on Token Based Computing, Bologna, Italy."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.sysarc.2019.01.015","article-title":"Decomposition of Distributed Edge Systems Based on the Petri Nets and Linear Algebra Technique","volume":"96","author":"Karatkevich","year":"2019","journal-title":"J. Syst. Archit."},{"key":"ref_30","unstructured":"Guo, C., Zhang, Y., Chen, L., Zhou, T., Li, X., Wang, M., and Wen, Z. (2012, January 20\u201323). A Novel Application of FPGA-Based Partial Dynamic Reconfiguration System with CBSC. Proceedings of the 2012 VIII Southern Conference on Programmable Logic, Bento Gon\u00e7alves, Brazil."},{"key":"ref_31","unstructured":"Wang, L., and Feng-yan, W. (2009, January 21\u201322). Dynamic Partial Reconfiguration in FPGAs. Proceedings of the 3rd International Symposium on Intelligent Information Technology Application, Nanchang, China."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"32376","DOI":"10.1109\/ACCESS.2018.2836858","article-title":"Dynamic Partial Reconfiguration of Concurrent Control Systems Specified by Petri Nets and Implemented in Xilinx FPGA Devices","volume":"6","year":"2018","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wi\u015bniewski, R. (2021). Design of Petri Net-Based Cyber-Physical Systems Oriented on the Implementation in Field Programmable Gate Arrays. Energies, 14.","DOI":"10.3390\/en14217054"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1093\/comjnl\/43.3.224","article-title":"Modular Analysis of Petri Nets","volume":"43","author":"Christensen","year":"2000","journal-title":"Comput. J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1109\/TCST.2017.2692204","article-title":"Prototyping of Concurrent Control Systems with Application of Petri Nets and Comparability Graphs","volume":"26","author":"Karatkevich","year":"2018","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_36","unstructured":"Clarke, E.M., Grumberg, O., and Peleg, D. (1999). Model Checking, MIT Press."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1109\/9.989151","article-title":"Overlapping Decompositions and Expansions of Petri Nets","volume":"47","author":"Aybar","year":"2002","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1007\/s10559-006-0044-0","article-title":"Compositional Analysis of Petri Nets","volume":"42","author":"Zaitsev","year":"2006","journal-title":"Cybern. Syst. Anal."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"De Michelis, G., and Diaz, M. (1995). Application and Theory of Petri Nets 1995, Springer.","DOI":"10.1007\/3-540-60029-9"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1299\/jamdsm.1.262","article-title":"Petri Net Modeling and Decomposition Method for Solving Production Scheduling Problems","volume":"1","author":"Nishi","year":"2007","journal-title":"J. Adv. Mech. Des. Syst. Manuf."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Costa, A., and Gomes, L. (2009, January 23\u201326). Petri Net Partitioning Using Net Splitting Operation. Proceedings of the 2009 7th IEEE International Conference on Industrial Informatics, Cardiff, UK.","DOI":"10.1109\/INDIN.2009.5195804"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Kordon, F., and Moldt, D. (2016). Application and Theory of Petri Nets and Concurrency, Springer.","DOI":"10.1007\/978-3-319-39086-4"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.ins.2019.01.029","article-title":"Deadlock Analysis and Control Using Petri Net Decomposition Techniques","volume":"482","author":"Zhong","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Janicki, R., Sidorova, N., and Chatain, T. (2020). Application and Theory of Petri Nets and Concurrency, Springer.","DOI":"10.1007\/978-3-030-51831-8"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1360","DOI":"10.1109\/TSMC.2017.2703950","article-title":"Structural Decomposition and Decentralized Control of Petri Nets","volume":"48","author":"Ye","year":"2018","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_46","unstructured":"Karatkevich, A. (2007). Dynamic Analysis of Petri Net-Based Discrete Systems, Springer. Lecture Notes in Control and Information Sciences."}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/13\/12\/7137\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:55:02Z","timestamp":1760126102000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/13\/12\/7137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,14]]},"references-count":46,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["app13127137"],"URL":"https:\/\/doi.org\/10.3390\/app13127137","relation":{},"ISSN":["2076-3417"],"issn-type":[{"value":"2076-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,14]]}}}