Some observations on supervisory policies that enforce liveness in partially controlled Free-choice Petri nets

Research output: Contribution to journalConference article

Abstract

Every arc from a place to a transition in a Free-Choice Petri net (FCPN) is either the unique output arc of the place, or, the unique input arc to the transition [M.H.T. Hack, Analysis of production schemata by Petri nets, Master's thesis, Massachusetts Institute of Technology, February 1972; W. Reisig, Petri Nets, Springer-Verlag, Berlin, 1985; T. Murata, Petri nets: properties, analysis and applications, Proc. IEEE 77 (4) (1989) 541-580]. We consider FCPNs that are not live [J.L. Peterson, Petri Net Theory and the Modeling of Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981; W. Reisig, Petri Nets, Springer-Verlag, Berlin, 1985; T. Murata, Petri nets: properties, analysis and applications, Proc. IEEE 77 (4) (1989) 541-580], and we investigate the existence of supervisory policies that can enforce liveness in partially controlled FCPNs. The external agent, or supervisor, can only prevent the firing of some (i.e. not all) transitions in a partially controlled FCPN. We first present an observation on supervisory policies that enforce liveness in partially-controlled FCPNs. Using this observation, we solve the supervisory synthesis problem for the family of c hoice-controlled FCPNs, defined in this paper. We then identify a new, sub-class of partially-controlled FCPNs that posses an easily-characterized (and easily-enforced) supervisory policy that enforces liveness.

Original languageEnglish (US)
Pages (from-to)266-274
Number of pages9
JournalMathematics and Computers in Simulation
Volume70
Issue number5-6
DOIs
StatePublished - Feb 24 2006
EventComputational Engineering in Systems Applications -
Duration: Jul 9 2003Jul 11 2003

Fingerprint

Liveness
Petri nets
Petri Nets
Arc of a curve
Observation
Policy
Supervisory personnel
Schema
Synthesis
Output
Modeling

Keywords

  • Petri nets
  • Supervisory control

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

Cite this

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title = "Some observations on supervisory policies that enforce liveness in partially controlled Free-choice Petri nets",
abstract = "Every arc from a place to a transition in a Free-Choice Petri net (FCPN) is either the unique output arc of the place, or, the unique input arc to the transition [M.H.T. Hack, Analysis of production schemata by Petri nets, Master's thesis, Massachusetts Institute of Technology, February 1972; W. Reisig, Petri Nets, Springer-Verlag, Berlin, 1985; T. Murata, Petri nets: properties, analysis and applications, Proc. IEEE 77 (4) (1989) 541-580]. We consider FCPNs that are not live [J.L. Peterson, Petri Net Theory and the Modeling of Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981; W. Reisig, Petri Nets, Springer-Verlag, Berlin, 1985; T. Murata, Petri nets: properties, analysis and applications, Proc. IEEE 77 (4) (1989) 541-580], and we investigate the existence of supervisory policies that can enforce liveness in partially controlled FCPNs. The external agent, or supervisor, can only prevent the firing of some (i.e. not all) transitions in a partially controlled FCPN. We first present an observation on supervisory policies that enforce liveness in partially-controlled FCPNs. Using this observation, we solve the supervisory synthesis problem for the family of c hoice-controlled FCPNs, defined in this paper. We then identify a new, sub-class of partially-controlled FCPNs that posses an easily-characterized (and easily-enforced) supervisory policy that enforces liveness.",
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N2 - Every arc from a place to a transition in a Free-Choice Petri net (FCPN) is either the unique output arc of the place, or, the unique input arc to the transition [M.H.T. Hack, Analysis of production schemata by Petri nets, Master's thesis, Massachusetts Institute of Technology, February 1972; W. Reisig, Petri Nets, Springer-Verlag, Berlin, 1985; T. Murata, Petri nets: properties, analysis and applications, Proc. IEEE 77 (4) (1989) 541-580]. We consider FCPNs that are not live [J.L. Peterson, Petri Net Theory and the Modeling of Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981; W. Reisig, Petri Nets, Springer-Verlag, Berlin, 1985; T. Murata, Petri nets: properties, analysis and applications, Proc. IEEE 77 (4) (1989) 541-580], and we investigate the existence of supervisory policies that can enforce liveness in partially controlled FCPNs. The external agent, or supervisor, can only prevent the firing of some (i.e. not all) transitions in a partially controlled FCPN. We first present an observation on supervisory policies that enforce liveness in partially-controlled FCPNs. Using this observation, we solve the supervisory synthesis problem for the family of c hoice-controlled FCPNs, defined in this paper. We then identify a new, sub-class of partially-controlled FCPNs that posses an easily-characterized (and easily-enforced) supervisory policy that enforces liveness.

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