## 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 language | English (US) |
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Pages (from-to) | 373-405 |

Number of pages | 33 |

Journal | Discrete Event Dynamic Systems: Theory and Applications |

Volume | 31 |

Issue number | 3 |

DOIs | |

State | Published - Sep 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