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More on Maximally Permissive Similarity Control of Discrete Event Systems

Yu Wang, Zhaohui Zhu, Rob van Glabbeek, Shigemasa Takai, Jinjin Zhang, Lixing Tan

TL;DR

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.

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.

More on Maximally Permissive Similarity Control of Discrete Event Systems

TL;DR

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.

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.
Paper Structure (6 sections, 11 theorems, 27 equations, 8 figures)

This paper contains 6 sections, 11 theorems, 27 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. A Counterexample
  4. Saturated $(G,R)$-automata
  5. Flaws in 2022Synthesis9029606
  6. Conclusion

Key Result

Proposition 1

Kimura2014Maximally Let $G=(X,\Sigma, \longrightarrow, X_0)$ and $R=(Z,\Sigma, \longrightarrow, Z_0)$ be two automata. $(prop-fixpoint-a)$ For any $\Phi\subseteq X\times Z$, $\Phi$ is a $\Sigma_{uc}$-simulation from $G$ to $R$ iff $\Phi=F_{(G,R)}(\Phi)$ and $\forall x_0\in X_0\ \exists z_0\in Z_0 (

Figures (8)

  • Figure 1: The system $G$
  • Figure 2: Another model for $G$
  • Figure 3: The plant $G$ (left) and specification $R$ (right)
  • Figure 4: The supervisor $S$ (left) and reachable part of the supervised plant $S||G$ (right)
  • Figure 5: The plant $G$ (left) and specification $R$ (right)
  • ...and 3 more figures

Theorems & Definitions (27)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Proposition 1
  • Definition 5
  • Lemma 1
  • Example 1
  • Definition 6
  • Example 2
  • ...and 17 more