Supervisory Control of Fuzzy Discrete Event Systems

Title: Supervisory Control of Fuzzy Discrete Event Systems

Research Question: How can we extend the concept of controllability in discrete event systems to incorporate fuzzy sets, allowing for uncertainty in state transitions and control strategies?

Methodology: The researchers propose a framework for supervisory control of fuzzy discrete event systems. They use fuzzy automata to model the systems, where the behavior is described by fuzzy languages. The supervisors are event-feedback and can disable controllable events with any degree. They present a necessary and sufficient condition for a fuzzy language to be controllable, and study the supremal controllable fuzzy sub-language and the infimal controllable fuzzy super-language given a pre-specified desired fuzzy language.

Results: The researchers provide numerical examples to illustrate their findings. They show that their framework generalizes the Ramadge-Wonham framework and reduces to it when membership grades in all fuzzy languages are either 0 or 1.

Implications: The extension of controllability to fuzzy systems allows for a more realistic modeling of situations where the state transitions and control strategies are uncertain or imprecise. This can lead to improved control strategies and better understanding of complex systems. The framework provides a solid theoretical basis for fuzzy supervisory control of discrete event systems and opens up new areas for further research.

Keywords: Fuzzy Discrete Event Systems, Supervisory Control, Controllability, Fuzzy Languages, Fuzzy Automata

Link to Article: https://arxiv.org/abs/0405040v1 Authors: arXiv ID: 0405040v1