Petri Nets

  • Christos G. Cassandras
  • Stéphane Lafortune
Part of the The Kluwer International Series on Discrete Event Dynamic Systems book series (DEDS, volume 11)


An alternative to automata for untimed models of DES is provided by Petri nets. These models were first developed by C. A. Petri in the early 1960’s. As we will see, Petri nets are related to automata in the sense that they also explicitly represent the transition function of DES. Like an automaton, a Petri net is a device that manipulates events according to certain rules. One of its features is that it includes explicit conditions under which an event can be enabled; this allows the representation of very general DES whose operation depends on potentially complex control schemes. This representation is conveniently described graphically, at least for small systems, resulting in Petri net graphs; Petri net graphs are intuitive and capture a lot of structural information about the system. We will see that an automaton can always be represented as a Petri net; on the other hand, not all Petri nets can be represented as finite-state automata. Consequently, Petri nets can represent a larger class of languages than the class of regular languages, R. Another motivation for considering Petri net models of DES is the body of analysis techniques that have been developed for studying them. Such techniques cover not only untimed Petri net models but timed Petri net models as well; in this regard, we will see in the next chapter that there is a well-developed theory, called the “max-plus algebra,” for a certain class of timed Petri nets (cf. Section 5.4). Finally, we mention that Grafcet, the widely-used programming language for programmable logic controllers (or PLCs) used in industrial automation, is inspired by Petri nets.


Coverability Tree Regular Language Reachable State State Transition Diagram State Transition Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Selected References

Introductory books or survey papers on Petri nets

  1. David, R., and H. Alla, Petri Nets & Grafcet: Tools for Modelling Discrete Event Systems, Prentice-Hall, New York, 1992.MATHGoogle Scholar
  2. Murata, T., “Petri Nets: Properties, Analysis and Applications,” Proceedings of the IEEE, Vol. 77, No. 4, pp. 541–580, 1989.CrossRefGoogle Scholar
  3. Peterson, J.L., Petri Net Theory and the Modeling of Systems, Prentice Hall, Englewood Cliffs, 1981.Google Scholar

Control of Petri nets

  1. Holloway, L.E., B.H. Krogh, and A. Giva, “A Survey of Petri Net Methods for Controlled Discrete Event Systems,” Journal of Discrete Event Dynamic Systems: Theory and Applications, Vol. 7, No. 2, pp. 151–190, April 1997.MATHCrossRefGoogle Scholar
  2. Moody, J.O., and P.J. Antsaklis, Supervisory Control of Discrete Event Systems Using Petri Nets, Kluwer Academic Publishers, Boston, 1998.MATHCrossRefGoogle Scholar


  1. Desrochers, A.A., and R.Y. Al-Jaar, Applications of Petri Nets in Automated Manufacturing Systems: Modeling, Control, and Performance Analysis, IEEE Press, Piscataway, NJ, 1995.Google Scholar
  2. Giva, A., and F. DiCesare, “Blocking and Controllability of Petri Nets in Supervisory Control,” IEEE Transactions on Automatic Control, Vol. 39, No. 4, pp. 818–823, April 1994.CrossRefGoogle Scholar
  3. Sreenivas, R.S., and B.H. Krogh, “On Petri Net Models of Infinite State Supervisors,” IEEE Transactions on Automatic Control, Vol. 37, No. 2, pp. 274–277, February 1992.MathSciNetCrossRefGoogle Scholar
  4. Zhou, M.C., and F. DiCesare, Petri Net Synthesis for Discrete Event Control of Manufacturing Systems, Kluwer Academic Publishers, Boston, 1993.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Christos G. Cassandras
    • 1
  • Stéphane Lafortune
    • 2
  1. 1.Boston UniversityUSA
  2. 2.The University of MichiganUSA

Personalised recommendations