Supervisory Control of Fuzzy Discrete Event Systems

TL;DR

This paper extends supervisory control theory to fuzzy discrete event systems, providing necessary and sufficient conditions for controllability, and generalizes classical frameworks to handle fuzzy automata with partial controllability.

Contribution

It introduces a fuzzy automata-based supervisory control framework, extending classical discrete event systems theory to incorporate fuzziness and partial controllability.

Findings

Established a necessary and sufficient condition for fuzzy language controllability.

Analyzed the supremal controllable fuzzy sublanguage and infimal controllable fuzzy superlanguage.

Demonstrated the framework with numerical examples.

Abstract

In order to cope with situations in which a plant's dynamics are not precisely known, we consider the problem of supervisory control for a class of discrete event systems modelled by fuzzy automata. The behavior of such discrete event systems is described by fuzzy languages; the supervisors are event feedback and can disable only controllable events with any degree. The concept of discrete event system controllability is thus extended by incorporating fuzziness. In this new sense, we present a necessary and sufficient condition for a fuzzy language to be controllable. We also study the supremal controllable fuzzy sublanguage and the infimal controllable fuzzy superlanguage when a given pre-specified desired fuzzy language is uncontrollable. Our framework generalizes that of Ramadge-Wonham and reduces to Ramadge-Wonham framework when membership grades in all fuzzy languages must be either 0 or 1. The theoretical development is accompanied by illustrative numerical examples.