On computing the supremal right-closed control invariant subset of a right-closed set of markings for an arbitrary petri net

Roshanak Khaleghi, Ramavarapu S. Sreenivas

Research output: Contribution to journalArticlepeer-review

Abstract

A set of non-negative integral vectors is said to be right-closed if the presence of a vector in the set implies all term-wise larger vectors also belong to the set. A set of markings is control invariant with respect to a Petri Net (PN) structure if the firing of any uncontrollable transition at any marking in this set results in a new marking that is also in the set. Every right-closed set of markings has a unique supremal control invariant subset, which is the largest subset that is control invariant with respect to the PN structure. This subset is not necessarily right-closed. In this paper, we present an algorithm that computes the supremal right-closed control invariant subset of a right-closed of markings with respect to an arbitrary PN structure. This set plays a critical role in the synthesis of Liveness Enforcing Supervisory Policies (LESPs) for a class of PN structures, and consequently, the proposed algorithm plays a key role in the synthesis of LESPs for this class of PN structures.

Original languageEnglish (US)
JournalDiscrete Event Dynamic Systems: Theory and Applications
DOIs
StateAccepted/In press - 2021

Keywords

  • Control Invariance
  • Petri Nets
  • Right-closed sets
  • Supervisory Control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Electrical and Electronic Engineering

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