On a minimally restrictive supervisory policy that enforces liveness in partially controlled free choice Petri Nets

Research output: Contribution to journalConference article

Abstract

A Petri Net (PN) is said to be live if it is possible to fire any transition from every reachable marking, although not necessarily immediately. Under appropriate conditions, a non-live PN can be made live via supervision. Under this paradigm an external-agent, the supervisor, prevents the firing of certain transitions at each reachable marking so as to enforce liveness. A PN is partially controlled if the supervisor can prevent the firing of only a subset of transitions. A Free Choice Petri net (FCPN) is a PN where every arc from a place to a transition is either than unique output arc from that place, or, it is the unique input arc to the transition. In this paper we show for each partially controlled FCPN that can be made live via supervision, any marking that is reachable under a policy that enforces liveness should cover (with respect to the standard partial ordering of vectors) a member of a specific, finite set of minimal-markings. Assuming this set is readily available, this observation is used to (i) test the existence, and (ii) to synthesize a minimally restrictive supervisory policy that enforces liveness in a partially controllable FCPN. We suggest investigations into the computation of this specific, finite set of minimal markings as a future research topic.

Original languageEnglish (US)
Pages (from-to)2651-2656
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume3
StatePublished - Dec 1 2000
Event39th IEEE Confernce on Decision and Control - Sysdney, NSW, Australia
Duration: Dec 12 2000Dec 15 2000

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Liveness
Petri nets
Petri Nets
Arc of a curve
Supervisory personnel
Finite Set
Partial ordering
Policy
Immediately
Paradigm
Cover
Subset
Output

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

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abstract = "A Petri Net (PN) is said to be live if it is possible to fire any transition from every reachable marking, although not necessarily immediately. Under appropriate conditions, a non-live PN can be made live via supervision. Under this paradigm an external-agent, the supervisor, prevents the firing of certain transitions at each reachable marking so as to enforce liveness. A PN is partially controlled if the supervisor can prevent the firing of only a subset of transitions. A Free Choice Petri net (FCPN) is a PN where every arc from a place to a transition is either than unique output arc from that place, or, it is the unique input arc to the transition. In this paper we show for each partially controlled FCPN that can be made live via supervision, any marking that is reachable under a policy that enforces liveness should cover (with respect to the standard partial ordering of vectors) a member of a specific, finite set of minimal-markings. Assuming this set is readily available, this observation is used to (i) test the existence, and (ii) to synthesize a minimally restrictive supervisory policy that enforces liveness in a partially controllable FCPN. We suggest investigations into the computation of this specific, finite set of minimal markings as a future research topic.",
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AB - A Petri Net (PN) is said to be live if it is possible to fire any transition from every reachable marking, although not necessarily immediately. Under appropriate conditions, a non-live PN can be made live via supervision. Under this paradigm an external-agent, the supervisor, prevents the firing of certain transitions at each reachable marking so as to enforce liveness. A PN is partially controlled if the supervisor can prevent the firing of only a subset of transitions. A Free Choice Petri net (FCPN) is a PN where every arc from a place to a transition is either than unique output arc from that place, or, it is the unique input arc to the transition. In this paper we show for each partially controlled FCPN that can be made live via supervision, any marking that is reachable under a policy that enforces liveness should cover (with respect to the standard partial ordering of vectors) a member of a specific, finite set of minimal-markings. Assuming this set is readily available, this observation is used to (i) test the existence, and (ii) to synthesize a minimally restrictive supervisory policy that enforces liveness in a partially controllable FCPN. We suggest investigations into the computation of this specific, finite set of minimal markings as a future research topic.

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