Comments on 'Maximally permissive supervisor synthesis based on a new constraint transformation method'

TL;DR

This paper critiques a proposed method for supervisor synthesis in Petri nets, providing a counterexample that challenges the validity of a key theorem and highlighting the importance of rigorous validation in control design.

Contribution

It offers a critical analysis of Luo et al.'s method, demonstrating a flaw in their theorem through a counterexample, thus contributing to more accurate supervisor synthesis techniques.

Findings

Counterexample invalidates the theorem

Highlights need for rigorous validation

Questions the correctness of the proposed method

Abstract

Luo et al. proposed a new method to design the maximally permissive and efficient supervisor for enforcing linear constraints on an ordinary Petri net with uncontrollable transitions. In order to develop this method, Theorem 3 is given. It is claimed that 'a linear constraint can be equivalently transformed at an uncontrollable transition into a disjunction of weakly admissible ones.' However, this result is erroneous. In this correspondence paper, a counterexample contradicting it is presented.