Skip to main content

Part of the book series: Advances in Industrial Control ((AIC))

  • 1468 Accesses

Abstract

This section introduces the analysis algorithms of concurrent control systems described by interpreted Petri nets. Such a process is applied to the net in order to c heck its dynamic and structural properties. First, we shall review the most popular analysis method of the dynamic behavior of the net, based on the integer linear algebra (p-invariants computation). Next, concurrency and sequentiality aspects of Petri nets will be discussed in details. We shall present novel analysis methods that apply graph and hypergraph theories.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Banaszak Z, Kuś J, Adamski M (1993) Petri nets: modeling, control and synthesis of discrete systems. Higher School of Engineering Publishing House, Zielona Góra (in Polish)

    Google Scholar 

  2. Berthelot G (1986) Checking properties of nets using transformation. In: Advances in Petri Nets’85. Lecture notes in computer science, vol 222. Springer, pp 19–40

    Google Scholar 

  3. Berthelot G, Roucairol C (1976) Reduction of Petri nets. Mathematical foundations of computer science, vol 45. Lecture notes in computer science. Springer, Berlin, pp 202–209

    Google Scholar 

  4. Berthelot G, Roucairol C, Valk R (1980) Reduction of nets and parallel programs. In: Lecture Notes in computer science, vol. 84. Springer, pp 277–290

    Google Scholar 

  5. Buchholz P, Kemper P (2002) Hierarchical reachability graph generation for Petri nets. Formal Methods Syst Des 21(3):281–315

    Article  MathSciNet  MATH  Google Scholar 

  6. Clarke EM, Grumberg O, Minea M, Peled DA (1999) State space reduction using partial order techniques. STTT 2(3):279–287

    Article  MATH  Google Scholar 

  7. Cortadella J (2002) Logic synthesis for asynchronous controllers and interfaces. Springer series in advanced microelectronics. Springer, Berlin, New York

    Google Scholar 

  8. Cortadella J, Kishinevsky M, Lavagno L, Yakovlev A (1998) Deriving Petri nets from finite transition systems. IEEE Trans Comput 47(8):859–882

    Article  MathSciNet  Google Scholar 

  9. Cortadella J, Reisig W (eds) 25th international conference applications and theory of Petri Nets 2004, ICATPN 2004, Bologna, Italy, 21–25 Jun 2004, Proceedings. Lecture notes in computer science, vol 3099. Springer

    Google Scholar 

  10. Desel J, Esparza J (1995) Free choice Petri nets. Cambridge University Press, New York, NY, USA

    Book  MATH  Google Scholar 

  11. Dong M, Chen FF (2001) Process modeling and analysis of manufacturing supply chain networks using object-oriented Petri nets. Rob Comput Integr Manuf 17(1):121–129

    Article  Google Scholar 

  12. Finkel A (1991) The minimal coverability graph for Petri nets. In: Advances in Petri Nets 1993, Papers from the 12th international conference on applications and theory of Petri nets, Gjern, Denmark, June 1991, pp 210–243

    Google Scholar 

  13. Holloway LE, Krogh BH (1990) Synthesis of feedback control logic for a class of controlled Petri nets. IEEE Trans Autom Control 35(5):514–523

    Article  MathSciNet  MATH  Google Scholar 

  14. Janicki R, Koutny M (1991) Using optimal simulations to reduce reachability graphs. In: Clarke EM, Kurshan RP (eds) Proceedings of the 2nd international conference on computer-aided verification CAV’90. LNCS, vol 531. Springer, London, pp 166–175

    Google Scholar 

  15. Karatkevich A (2007) Dynamic analysis of Petri net-based discrete systems. Lecture Notes in Control and Information Sciences, vol 356. Springer, Berlin

    Google Scholar 

  16. Klas G (1992) Hierarchical solution of generalized stochastic Petri nets by means of traffic processes. In: Jensen K (ed) Proceedingsof the 13th international conference on application and theory of Petri nets, Sheffield. Lecture notes in computer science, vol 616, pp 279–298

    Google Scholar 

  17. Kovalyov A (1992) Concurrency relation and the safety problem for Petri nets. In: Jensen K (ed) Proceedings of the 13th international conference on application and theory of Petri nets 1992. LNCS, vol 616. Springer, pp 299–309

    Google Scholar 

  18. Kovalyov A, Esparza J (1995) A polynomial algorithm to compute the concurrency relation of free-choice signal transition graphs. In: Proceedings of the international workshop WODES, pp 1–6

    Google Scholar 

  19. Lautenbach K (1986) Linear algebraic techniques for place/transition nets. In: Brauer W, Reisig W, Rozenberg G (eds) Advances in Petri nets. Lecture notes in computer science, vol 254. Springer, pp 142–167

    Google Scholar 

  20. Martinez J, Silva M (1982) A simple and fast algorithm to obtain all invariants of a generalized Petri net. In: Selected papers from the European workshop on applicational and theory of Petri nets, 1982. Springer, London, UK, pp 301–310

    Google Scholar 

  21. Memmi G, Roucairol G (1979) Linear algebra in net theory. In: Net theory and applications, proceedings of the advanced course on general net theory of processes and systems, Hamburg, 8–19 Oct 1979, pp 213–223

    Google Scholar 

  22. Montano L, García-Izquierdo, Villarroel J, Using the time Petri net formalism for specification, validation, and code generation in robot-control applications. Int J Rob Res 19:59–76

    Google Scholar 

  23. Moody J, Yamalidou K, Lemmon M, Antsaklis P (1994) Feedback control of Petri nets based on place invariants. In: Proceedings of the 33rd IEEE conference on decision and control, 1994, vol 3. IEEE, pp 3104–3109

    Google Scholar 

  24. Murata T (1989) Petri nets: properties, analysis and applications. Proc IEEE 77:548–580

    Article  Google Scholar 

  25. Pastor E, Cortadella J (1998) Efficient encoding schemes for symbolic analysis of Petri nets. In: DATE’98, pp 790–795

    Google Scholar 

  26. Peterson JL (1981) Petri net theory and the modeling of systems. Prentice Hall PTR, Upper Saddle River, NJ, USA

    MATH  Google Scholar 

  27. Silva M (1993) Introducing Petri nets. In: Practice of Petri nets in manufacturing. Springer, Netherlands, pp 1–62

    Google Scholar 

  28. Silva M, Terue E, Colom JM (1998) Linear algebraic and linear programming techniques for the analysis of place/transition net systems. Springer, Berlin, Heidelberg, pp 309–373

    Google Scholar 

  29. Valmari A (1991) Stubborn sets for reduced state space generation. In: Advances in Petri nets 1990. Lecture notes in computer science, vol 483. Springer, Berlin, Germany, pp 491–515

    Google Scholar 

  30. Varpaaniemi K (1998) On the Stubborn Set Method in Reduced State Space Generation. Ph.D. thesis, Helsinki University of Technology, Department of Computer Science and Engineering

    Google Scholar 

  31. Wiśniewska M (2012) Application of hypergraphs in decomposition of discrete systems. Lecture notes in control and computer science, vol 23. University of Zielona Góra Press, Zielona Góra

    Google Scholar 

  32. Wiśniewska M, Adamski M (2006) Hypergraphs in the state space analysis of concurrent automata described by Petri nets. Meas Autom Monit 52(7 bis):62–64 (in Polish)

    Google Scholar 

  33. Wiśniewski R, Stefanowicz Ł, Bukowiec A, Lipiński J (2014) Theoretical aspects of Petri nets decomposition based on invariants and hypergraphs, Zhangjiajie, China. Lecture notes in electrical engineering, vol 308, pp 371–376

    Google Scholar 

  34. Yakovlev A, Gomes L, Lavagno L (2000) Hardware design and Petri nets. Springer

    Google Scholar 

  35. Zakrevskij A, Pottosin Y, Cheremisinova L (2009) Design of logical control devices. TUT Press, Moskov

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Remigiusz Wiśniewski .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Wiśniewski, R. (2017). Analysis of Concurrent Control Systems. In: Prototyping of Concurrent Control Systems Implemented in FPGA Devices. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-45811-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45811-3_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45810-6

  • Online ISBN: 978-3-319-45811-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics