Skip to main content
Springer Nature Link
Log in

Diagnosability of Petri nets with observation graphs

  • Published:
Discrete Event Dynamic Systems Aims and scope Submit manuscript

Abstract

This paper addresses the problem of diagnosability for dynamic discrete event systems modeled with bounded or unbounded Petri nets that are deadlock-free and monitored with sensor configurations with marking and event measurements. The proposed method gives necessary and sufficient conditions for diagnosability. It is based on the transformation of the coverability graph into an observation graph that encodes all observation sequences of measured markings and events with respect to the sensor configuration. This graph also encodes all sequences of transitions that may fire from any reachable marking of the Petri net. Diagnosability is determined by analyzing the paths and circuits in the observation graph. The method is illustrated with several examples of bounded or unbounded Petri nets.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Basile F, Chiacchio P, De Tommasi G (2009) An efficient approach for online diagnosis of discrete event systems. IEEE Trans Aut Contr 54(4):748–759

    Article  MathSciNet  Google Scholar 

  • Basile F, Chiacchio P, De Tommasi G (2012) On K-diagnosability of Petri nets via integer linear programming. Autom 48:2047–2058

    Article  MathSciNet  MATH  Google Scholar 

  • Cabasino MP, Giua A, Seatzu C (2010) Fault detection for discrete event systems using Petri nets with unobservable transitions. Autom 46(9):1531–1539

    Article  MathSciNet  MATH  Google Scholar 

  • Cabasino MP, Giua A, Pocci M, Seatzu C (2011) Discrete event diagnosis using labeled Petri nets. An application to manufacturing systems. Cont Eng Pract 19:989–1001

    Article  Google Scholar 

  • Cabasino MP, Giua A, Lafortune S, Seatzu C (2012) A new approach for diagnosability analysis of Petri nets using verifier net. IEEE Trans Aut Cont 57(12):3104–3117

    Article  MathSciNet  Google Scholar 

  • Chu F, Xie C-L (1997) Deadlock analysis of Petri nets using siphons and mathematical programming. IEEE Trans Rob And Auto 13(6):793–804

    Article  Google Scholar 

  • Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to Algorithms. MIT Press, third edition.

  • Ding ZJ, Jiang CJ, Zhou MC (2008) Deadlock checking for one-place unbounded Petri nets based on modified reachability trees. IEEE Trans Syst Man Cybern B 38(3):881–883

    Article  Google Scholar 

  • Dotoli M, Fanti MP, Mangini AM, Ukovich W (2009) On-line fault detection in discrete event systems by Petri nets and integer linear programming. Autom 45:2665–2672

    Article  MathSciNet  MATH  Google Scholar 

  • Genc S, Lafortune S (2007) Distributed diagnosis of place-bordered Petri nets. IEEE Trans Aut Sci Eng 4(2):206–219

    Article  Google Scholar 

  • Krutz RL (2005) Securing SCADA Systems, Wiley

  • Lefebvre D (2008) Firing sequences estimation in vector space over Z3 for ordinary Petri nets. IEEE Trans Syst Man Cyb Part A 38(6):1325–1336

    Article  Google Scholar 

  • Lefebvre D (2012a) Diagnosis with Petri nets according to partial events and states observation. Proc. IFAC - Safeprocess, Mexico City

    Google Scholar 

  • Lefebvre D (2012b) An algorithm of linear complexity for the diagnosis of discrete event systems. Proc. IFAC MIM, St Petersburg, pp 287–292

    Google Scholar 

  • Lefebvre D (2013) On-line fault diagnosis with partially observed Petri nets, to appear IEEE – TAC

  • Lefebvre D, Delherm C (2007) Diagnosis of DES with Petri net models. IEEE Trans Aut Sci Eng 4(1):114–118

    Article  Google Scholar 

  • Peterson JL (1981) Petri net theory and the modelling of systems. Prentice Hall, New Jersey

    MATH  Google Scholar 

  • Ramírez-Treviño A, Ruiz-Beltran E, Rivera-Rangel I, Lopez-Mellado E (2007) Online fault diagnosis of discrete event systems. A Petri net-based approach. IEEE Trans Aut Sci Eng 4(1):31–39

    Article  Google Scholar 

  • Ru Y, Hadjicostis CN (2009) Fault diagnosis in discrete event systems modeled by partially observed Petri nets. Discret Event Dyn Syst 19:551–575

    Article  MathSciNet  MATH  Google Scholar 

  • Ru Y, Wu W, Hadjicostis CN (2006) Comments on “A modified reachability tree approach to the analysis of unbounded Petri nets”. IEEE Trans Syst Man Cybern B 36(5):1210–1210

    Article  Google Scholar 

  • Tarjan R (1972) Depth-first search and linear graph algorithms. SIAM J Comput 1(2):146–160

    Article  MathSciNet  MATH  Google Scholar 

  • Tong Y, Li ZW, Giua A (2013) General observation structures for Petri nets, Proc. 18th IEEE Conference on Emerging Technologies & Factory Automation (IEEE - ETFA), Cagliary, Italy

  • Wang FY, Gao QY, Zhou MC (2004) A modified reachability tree approach to analysis of unbounded Petri nets. IEEE Trans Syst Man Cybern B 34(1):303–308

    Article  Google Scholar 

  • Wang SG, Zhou MC, Li ZW, Wang CY (2013) A new modified reachability tree approach and its applications to unbounded Petri nets. Trans Syst Man Cybern A 43(4):932–940

    Article  MathSciNet  Google Scholar 

  • Wu Y, Hadjicostis CN (2005) Algebraic approaches for fault identification in discrete-event systems. IEEE Trans Aut Contr 50(12):2048–2053

    Article  MathSciNet  Google Scholar 

  • Ye X, Zhou J, Song X (2003) On reachability graphs of Petri nets. Comput Electr Eng 29:263–272

    Article  MATH  Google Scholar 

  • Zhou MC, DiCesare F (1993) Petri net synthesis for discrete event control of manufacturing systems. Kluwer, Boston

    Book  MATH  Google Scholar 

  • Zhou MC, DiCesare F, Desrochers A (1992) A hybrid methodology for synthesis of Petri net models for manufacturing systems. IEEE - Trans Rob Auto 8(3):350–361

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. GREAH - University Le Havre, 75 rue Bellot, Le Havre, France

    D. Lefebvre & E. Leclercq

Authors
  1. D. Lefebvre
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. E. Leclercq
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to D. Lefebvre.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lefebvre, D., Leclercq, E. Diagnosability of Petri nets with observation graphs. Discrete Event Dyn Syst 26, 539–559 (2016). https://doi.org/10.1007/s10626-014-0207-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10626-014-0207-5

Keywords