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Fuzzy multimodel of timed Petri nets
S Hennequin1, D Lefebvre, A El Moudni
1Lab. de Syst. et Transp., Univ. de Technol. Belfort-Montbeliard.
Summary
This study introduces a fuzzy rule-based multimodel for discrete event systems (DES) using Petri nets. It demonstrates that classical sets precisely model discrete timed Petri nets, while fuzzy sets accurately describe continuous Petri nets.
Area of Science:
- Control Engineering
- Computer Science
- Fuzzy Systems
Background:
- Discrete Event Systems (DES) are crucial in modeling complex systems.
- Petri nets, including discrete timed and continuous variants, are common modeling tools.
- Existing models may lack precision for certain DES characteristics.
Purpose of the Study:
- To develop a fuzzy rule-based multimodel for DES.
- To precisely model discrete timed Petri nets and continuous Petri nets.
- To explore the control implications of the proposed fuzzy models.
Main Methods:
- Utilizing linear local fuzzy models to describe Petri net transition behavior.
- Applying the Takagi-Sugeno fuzzy model systematically.
- Employing classical sets for discrete timed Petri nets and fuzzy sets for continuous Petri nets.
Main Results:
- Achieved exact modeling for both discrete timed and continuous Petri nets.
- Demonstrated that classical sets are suitable for discrete timed Petri nets.
- Established that fuzzy sets are necessary for the exact description of continuous Petri nets.
Conclusions:
- The developed fuzzy rule-based multimodel offers an exact modeling approach for DES.
- The findings provide valuable insights for the control of timed Petri nets, including convergence properties.
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