Controllability conditions of resultant siphons in a class of Petri nets

Shou Guang Wang, Cheng Ying Wang, Meng Chu Zhou

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


Strict minimal siphons (SMSs) play a key role in the development of deadlock prevention policies by using Petri nets for flexible manufacturing systems (FMSs). In this paper, given two SMSs and their resultant siphon, the concept of key resource subsets is proposed which is shown to be the critical factor in deciding the controllability conditions of the latter. A necessary and sufficient condition is then proposed under which the resultant siphon can be always marked if its two SMSs are M-controlled, i.e., invariant controlled via the method proposed by Moody and Antsaklis. As for a resultant siphon that is composed by more than two composable SMSs, a sufficient condition is proposed under which it can be always marked if its SMSs are M-controlled. They are established by analyzing the structural characteristics and markings of the resource subnets in a class of Petri nets called L-S 3PR. When they are applied to some classes of S 3PR nets, i.e., those whose controlled ones are maximally permissive and live once their original SMSs are M-controlled, the number of monitors may be reduced. An FMS example is used to illustrate the application of the results.

Original languageEnglish (US)
Article number6075272
Pages (from-to)1206-1215
Number of pages10
JournalIEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans
Issue number5
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Software
  • Information Systems
  • Human-Computer Interaction
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


  • Automated manufacturing systems
  • Petri nets
  • deadlock
  • discrete event systems (DES)
  • siphon


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