Supervisory Control of Fuzzy Discrete Event Systems for Simulation Equivalence

TL;DR

This paper advances supervisory control theory for fuzzy discrete event systems by establishing fuzzy simulation equivalence, which offers greater expressiveness than fuzzy language equivalence, and provides methods for control and verification.

Contribution

It introduces fuzzy simulation and fuzzy simulation equivalence, along with controllability conditions, enhancing control design for fuzzy discrete event systems beyond traditional language-based methods.

Findings

Fuzzy simulation relations are formally defined and decidable.

Fuzzy simulation-based controllability is characterized as a necessary and sufficient condition.

Examples demonstrate the effectiveness of the proposed control methods.

Abstract

The supervisory control theory of fuzzy discrete event systems (FDESs) for fuzzy language equivalence has been developed. However, in a way, language equivalence has limited expressiveness. So if the given specification can not be expressed by language equivalence, then the control for language equivalence does not work. In this paper, we further establish the supervisory control theory of FDESs for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence. First, we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two FDESs. Then we present a method for deciding whether there is a fuzzy simulation or not. In addition, we also show several basic properties of fuzzy simulation relations. Afterwards, we put forward the notion of fuzzy simulation-based controllability, and particularly show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of FDESs. Moreover, we study the "range" control problem of FDESs. Some examples are given to illustrate the main results obtained.