Similarity-Based Supervisory Control of Discrete Event Systems

TL;DR

This paper introduces a metric-based extension to supervisory control theory for discrete event systems, allowing behavior modification based on similarity to handle uncontrollable events.

Contribution

It generalizes controllability to $ ext{d}$-controllability using a similarity metric, providing conditions and methods for optimizing system behavior.

Findings

Defined $ ext{d}$-controllability and its necessary and sufficient conditions

Analyzed properties of $ ext{d}$-controllable languages

Proposed an approach for optimizing realizations

Abstract

Due to the appearance of uncontrollable events in discrete event systems, one may wish to replace the behavior leading to the uncontrollability of pre-specified language by some quite similar one. To capture this similarity, we introduce metric to traditional supervisory control theory and generalize the concept of original controllability to $\ld$-controllability, where $\ld$ indicates the similarity degree of two languages. A necessary and sufficient condition for a language to be $\ld$-controllable is provided. We then examine some properties of $\ld$-controllable languages and present an approach to optimizing a realization.