Fuzzy multimodel of timed Petri nets

Abstract

This paper deals with discrete event systems (DES) modeled either by discrete timed Petri nets without conflict or by continuous Petri nets. A fuzzy rule-based multimodel is developed for this kind of system. The behavior of each Petri net transition is described by the combination of two linear local fuzzy models. Using the Takagi-Sugemo model in a systematic way, we define the exact modeling for both classes of timed Petri nets. As a result, we notice that classical sets result in the exact description of discrete timed Petri nets. On the contrary, only fuzzy sets are suitable to describe continuous Petri nets exactly. The proposed fuzzy multimodels are very interesting from a control point of view. In that sense, general results such as convergence for timed Petri nets are given.

An integrated control framework for flexible manufacturing systems

“…Various manufacturing system control frameworks that are based on fuzzy logic theory have been proposed by virtue of to their capability of collecting human knowledge and expertise and by dealing with uncertainties and complexities in the input-output relationship [28,29]. Moreover, fuzzy techniques are powerful tools to perform control system design and analysis [30]. Considering the extension of fuzzy control paradigms to manufacturing systems, most of the FMS applications deal with job sequencing and priority settings at machines [31].…”

“…Considering the extension of fuzzy control paradigms to manufacturing systems, most of the FMS applications deal with job sequencing and priority settings at machines [31]. In many real-time applications, fuzzy logic is used as an interface and decision-making tool of manufacturing systems with hybrid architectures where task behaviors of systems, such as, job selection, routing decisions, and dispatching, are considered and controlled as a DES while reactive behaviors such as, managing unexpected events, are considered as a continuous system and controlled with differential or difference equations [30][31][32].…”

Supervisory Control of Fuzzy Discrete Event Systems

“…Clearly, we see that (KE For any s ∈ E * , we now prove thatǨ(s) ≤ M(s). By Proposition 10, we get thať K(s) = (KE * uc )(s) ∧ L(s) = [∨ s1s2=s (K(s 1 ) ∧ E * uc (s 2 ))] ∧ L(s) =: (5). Since |s| is finite, there exist s ′ 1 and s ′ 2 satisfying s ′ 1 s ′ 2 = s such that ∨ s1s2=s (K(s 1 )∧E * uc (s 2 )) = K(s ′ 1 )∧E * uc (s ′ 2 ).…”

“…In recent years, fuzzy model such as fuzzy automata, fuzzy Petri nets, and fuzzy neural networks, as a complement to conventional models, has become an active research topic and found successful applications in many areas [2], [4], [16], [19], [21]. In terms of DES, fuzzy Petri net model has been investigated for many years [24], [5], [17]; however, to our knowledge, few efforts, except the work [12], [13], are made to consider the model and supervisory control following for fuzzy automata.…”