State-Based Control of Fuzzy Discrete Event Systems

TL;DR

This paper develops a state-based supervisory control approach for fuzzy discrete event systems, enabling more convenient control of system states and establishing conditions for controllability and state reachability.

Contribution

It introduces a novel state-based control framework, including controllability conditions and the relationship between event-based and state-based control for fuzzy systems.

Findings

All reachable fuzzy states can be identified under control.

A necessary and sufficient condition for fuzzy state controllability is provided.

The relationship between event-based and state-based control is clarified.

Abstract

To effectively represent possibility arising from states and dynamics of a system, fuzzy discrete event systems as a generalization of conventional discrete event systems have been introduced recently. Supervisory control theory based on event feedback has been well established for such systems. Noting that the system state description, from the viewpoint of specification, seems more convenient, we investigate the state-based control of fuzzy discrete event systems in this paper. We first present an approach to finding all fuzzy states that are reachable by controlling the system. After introducing the notion of controllability for fuzzy states, we then provide a necessary and sufficient condition for a set of fuzzy states to be controllable. We also find that event-based control and state-based control are not equivalent and further discuss the relationship between them. Finally, we examine the possibility of driving a fuzzy discrete event system under control from a given initial state to a prescribed set of fuzzy states and then keeping it there indefinitely.