On fluidification of Petri Nets: from discrete to hybrid and continuous models

Petri Nets (PNs) is a well-known modelling paradigm for discrete event systems (DES). As in other paradigms, hybrid and continuous PN formalisms have appeared in the literature, some of them being used in different engineering application domains. Hybridization may be obtained for example ‘‘by direct addition’’ of capabilities to model continuous subsystems. The approach adopted in this work is different: hybrid and continuous models appear because natural variables of a PN–DES model are transformed into non-negative reals. This relaxation may be quite reasonable when very populated or high traffic systems are considered. It is a classical relaxation applied to fight against the state explosion problem appearing when dealing with the analysis and synthesis of models. In tune with this, the paper presents ‘‘a biased’’ view of works in the hybrid PN arena. Partly an overview, this work revisits hybrid and continuous PNs, all of them being in essence hybrid models. Limitations to (partial) fluidification, and analysis and synthesis problems in this evolving field are considered. Several optimization problems (at design and at control) are also introduced here. # 2004 Published by Elsevier Ltd.

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