On the existence of supervisory policies that enforce liveness in discrete-event dynamic systems modeled by controlled petri nets

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Abstract

We consider discrete-state plants represented by controlled Petri nets (CtIPN's), where a subset of transitions can be prevented from firing by a super visor. A transition in a CtIPN can fire at a marking if there are sufficient tokens in its input places and it is permitted to fire by the supervisor. A CtIPN is live if it is possible to fire any transition from every marking that is reachable under supervision. In this paper we derive a necessary and sufficient condition for the existence of a supervisory policy that enforces liveness in CtIPN's. We show this condition cannot be tested for an arbitrary CtIPN. However, for bounded CtIPN's, or CtIPN's where each transition is individually controllable, we show the existence of a supervisory policy which enforces that livenessisdecidable. We also show the existence of a supervisory policy that enforces liveness is necessary and sufficient for the existence of a minimally restrictive supervisory policy.

Original languageEnglish (US)
Pages (from-to)928-945
Number of pages18
JournalIEEE Transactions on Automatic Control
Volume42
Issue number7
DOIs
StatePublished - 1997

Keywords

  • DEDS
  • Liveness
  • Petri nets
  • Supervisory control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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