More on Maximally Permissive Similarity Control of Discrete Event Systems

TL;DR

This paper examines the limitations of Takai's method for constructing maximally permissive supervisors in similarity control of discrete event systems, introduces a new automaton concept, and corrects previous flaws.

Contribution

It identifies issues in Takai's construction for non-image-finite specifications, introduces the saturated (G, R)-automaton, and provides corrected metatheorems for the similarity control problem.

Findings

Takai's method does not always work for non-image-finite specifications.

Introduction of the saturated (G, R)-automaton concept.

Correction of flaws in Takai's original work.

Abstract

Takai proposed a method for constructing a maximally permissive supervisor for the similarity control problem (IEEE Transactions on Automatic Control, 66(7):3197-3204, 2021). This paper points out that this construction does not(necessarily) work when the specification is not image-finite. Inspired by Takai's construction, the notion of a (saturated) (G, R)-automaton is introduced and metatheorems concerning (maximally permissive) supervisors for the similarity control problem are provided in terms of this notion. As an application of these metatheorems, the flaws in Takai's work are corrected.