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A Systems Theory View of Petri Nets

  • Alessandro Giua
  • Carla Seatzu
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 353)

Abstract

Petri nets are a family of powerful discrete event models whose interest has grown, within the automatic control community, in parallel with the development of the theory of discrete event systems. In this tutorial paper our goal is that of giving a flavor, by means of simple examples, of the features that make Petri nets a good model for systems theory and of pointing out at a few open areas for research. We focus on Place/Transitions nets, the simplest Petri net model. In particular we compare Petri nets with automata, and show that the former model has several advantages over the latter, not only because it is more general but also because it offers a better structure that has been used for developing computationally efficient algorithms for analysis and synthesis.

Keywords

Discrete Event Systems Petri Nets Models of Concurrency Controllability 

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References

  1. 1.
    Benasser A (2000) Reachability in Petri nets: an approach based on constraint programming, Ph.D. Thesis, Université de Lille, France (in French)Google Scholar
  2. 2.
    Bourdeaud’huy T, Yim P (2004) Synthse de rseaux de Petri partir d’exigences, Actes de la 5me conf. francophone de Modlisation et Simulation, (Nantes, France), 413–420, (in French)Google Scholar
  3. 3.
    Cabasino M P, Giua A, Seatzu C (2006) Identification of deterministic Petri nets, Proceedings of 8th International Workshop on Discrete Event Systems, Ann Arbor, Michigan, USAGoogle Scholar
  4. 4.
    Cabasino M P, Giua A, Seatzu C (2006) Identification of unbounded Petri nets from their coverability graph, Proceedings of 45th IEEE Conference on Decision and ControlGoogle Scholar
  5. 5.
    Cassandras C G, Lafortune S (1999) Introduction to Discrete Event Systems. Kluwer Academic PublishersGoogle Scholar
  6. 6.
    Chu F, Xie X (1997) Deadlock analysis of Petri nets using siphons and mathematical programming, IEEE Transactions on Robotics and Automation, 13: 793–804CrossRefGoogle Scholar
  7. 7.
    Corona D, Giua A, Seatzu C (2004) Marking estimation of Petri nets with silent transitions, Proceedings of 43rd IEEE Conference on Decision and ControlGoogle Scholar
  8. 8.
    Badouel E, Darondeau P (1998) Theory of regions. Lecture Notes in Computer Science: Lectures on Petri Nets I: Basic Models, Springer-Verlag, (eds. Reisig, W. and Rozenberg, G.), 1491: 529–586Google Scholar
  9. 9.
    David R, Alla H (2005) Discrete, continous and hybrid Petri nets. Springer Verlag, HeidelbergGoogle Scholar
  10. 10.
    DiCesare F, Harhalakis G, Proth J M, Silva M, Vernadat F B (1993) Practice of Petri Nets in Manufacturing. Chapman and HallGoogle Scholar
  11. 11.
    Ezpeleta J, Colom J M, Martinez J (1995) A PN based deadlock prevention policy for flexible manufacturing systems, IEEE Transactions on Robotics and Automation, 11: 173–184CrossRefGoogle Scholar
  12. 12.
    Gaubert S, Giua A (1999) Petri net languages and infinite subsets of ℕm, Journal of Computer and System Sciences, 59: 373–391zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Giua A, DiCesare F, Silva M (1992) Generalized mutual exclusion constraints on nets with uncontrollable transitions, Prooceedings of IEEE International Conference on Systems, Man and CyberneticsGoogle Scholar
  14. 14.
    Giua A, Seatzu C (2002) Observability of Place/Transition nets, IEEE Transactions on Automatic Control, 47: 1424–1437CrossRefMathSciNetGoogle Scholar
  15. 15.
    Giua A, Seatzu C, Basile F (2004) Observer based state-feedback control of timed Petri nets with deadlock recovery, IEEE Transactions on Automatic Control, 49: 17–29CrossRefMathSciNetGoogle Scholar
  16. 16.
    Giua A, Seatzu C (2005) Fault detection for discrete event systems using labeled Petri nets,” Proocedings of the 44th IEEE Conference on Decision and Control and European Control ConferenceGoogle Scholar
  17. 17.
    Giua A, Seatzu C (2005) Identification of free-labeled Petri nets via integer programming, Proocedings of the 44th IEEE Conference on Decision and Control and European Control ConferenceGoogle Scholar
  18. 18.
    Giua A, Corona D, Seatzu C (2005) State estimation of λ-free labeled Petri nets with contact-free nondeterministic transitions, Journal of Discrete Event Dynamic Systems, 15:85–108zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Hiraishi K (1992) Construction of a class of safe Petri nets by presenting firing sequences. Lecture Notes in Computer Science; 13th International Conference on Application and Theory of Petri Nets 1992, Sheffield, UK, Springer-Verlag, (ed. K. Jensen), 616: 244–262Google Scholar
  20. 20.
    Holloway L E, Krogh B H, Giua A (1997) A survey of Petri nets methods for controlled discrete event systems, Discrete Event Dynamic Systems, 7:151–190zbMATHCrossRefGoogle Scholar
  21. 21.
    Iordache M V, Moody J O, Antsaklis P J (2002) Synthesis of deadlock prevention supervisors using Petri nets, IEEE Transactions on Robotics and Automation, 18: 59–68CrossRefGoogle Scholar
  22. 22.
    Iordache MV, Antsaklis P J (2006) Supervisory Control of Concurrent Systems. A Petri Net Structural Approach. Series: Systems and Control: Foundations and Applications. BirkhuserGoogle Scholar
  23. 23.
    Lewis H R, Papadimitriou C H (1981) Elements of the Theory of Computation. Prentice-HallGoogle Scholar
  24. 24.
    Li Z, Zhou M (2004) Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems, IEEE Transactions on Systems, Man, Cybernetics, Part A, 34: 38–51CrossRefGoogle Scholar
  25. 25.
    Meda M E, Ramírez A, Malo A (1998) Identification in discrete event systems, Proceedings of 1998 IEEE International Conference on Systems, Man and Cybernetics, 740–745Google Scholar
  26. 26.
    Murata T (1977) State equation, controllability, and maximal matching of Petri nets, IEEE Transactions on Automatic Control, 22:412–416zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Murata T (1989) Petri nets: properties, analysis and applications, Proceedings IEEE 77: 541–580CrossRefGoogle Scholar
  28. 28.
    Park J, Reveliotis S A (2000) Algebraic synthesis of efficient deadlock avoidance policies for sequential resource allocation systems, IEEE Transactions on Automatic Control, 16: 190–195Google Scholar
  29. 29.
    Park J, Reveliotis S A (2002) Policy mixtures: a novel approach for enhancing the operational flexibility of resource allocation systems with alternate routings, IEEE Transactions on Robotics and Automation, 18:616–620CrossRefGoogle Scholar
  30. 30.
    Park J, Reveliotis S A (2002) Liveness-enforcing supervision for resource allocation systems with uncontrollable behavior and forbidden states, IEEE Transactions on Robotics and Automation, 18: 234–238CrossRefGoogle Scholar
  31. 31.
    Parigot M, Peltz E (1985) A logical formalism for the study of the finite behavior of Petri nets, in Advances in Petri Nets 1985, Lecture Notes in Computer Science 222, G. Rozenberg (ed.), Springer Verlag, 346–361Google Scholar
  32. 32.
    Peterson J L (1981) Petri Net Theory and the Modeling of Systems. Prentice-HallGoogle Scholar
  33. 33.
    Ramadge P J, Wonham W M (1989) The control of discrete event systems, Proceedings IEEE, 77: 81–98CrossRefGoogle Scholar
  34. 34.
    Recalde L (1998) Structural methods for the design and analysis of concurrent systems modeled with Place/Transition nets, PhD Thesis, DIIS. Univ. ZaragozaGoogle Scholar
  35. 35.
    Reveliotis S A (2005) Siphon-based characterization of liveness and liveness-enforcing supervision for sequential resource allocation systems, In Deadlock Resolution in Computer-Integrated Systems, M. Zhou and M. P. Fanti, (Eds), Marcel Dekker, Inc., 283–307Google Scholar
  36. 36.
    Silva M, Colom J M, Campos J (1992) Linear algebraic techniques for the analysis of Petri nets, Proceedings of International Symposium on Mathematical Theory of Networks and SystemsGoogle Scholar
  37. 37.
    Sreenivas R S, Krogh B H (1992) On Petri net models of infinite state supervisors, IEEE Transactions on Automatic Control, 37: 274–277CrossRefMathSciNetGoogle Scholar
  38. 38.
    Sreenivas R S (2002) On minimal representations of Petri net languages, 6th Workshop on Discrete Event Dynamic Systems, Zaragoza, Spain, 237–242Google Scholar
  39. 39.
    Viswanadham N, Narahari Y, Johnson T L (1990) Deadlock prevention and deadlock avoidance in flexible manufacturing systems using Petri net models, IEEE Transactions on Robotics and Automation, 6: 713–723CrossRefGoogle Scholar
  40. 40.
    Zhang L, Holloway L E (1995) Forbidden state avoidance, Proceedings of 33rd Allerton Conference, Monticello, Illinois, 146–155Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Alessandro Giua
    • 1
  • Carla Seatzu
    • 1
  1. 1.Dip. Ingegneria Elettrica ed ElettronicaUniversità di CagliariItaly

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