By Dr. René David, Pr. Hassane Alla (auth.)

ISBN-10: 3540224807

ISBN-13: 9783540224808

ISBN-10: 3540268219

ISBN-13: 9783540268215

This monograph provides a good written and obviously equipped creation within the typical tools of discrete, non-stop and hybrid Petri Nets. ranging from the fundamentals of Petri nets the publication imparts a correct realizing of continuing and hybrid Petri Nets. retaining the consistency of easy recommendations in the course of the textual content it introduces a unified framework for the entire types awarded. The ebook is a systematic monograph in addition to a didactic educational that is effortless to appreciate because of many workouts with ideas, precise figures and a number of other case reports. It demonstrates that Petri nets are a deep, useful and alive box very important for researchers, engineers and graduate scholars in engineering and machine science.

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Extra info for Discrete, Continuous, and Hybrid Petri Nets

Example text

The extended and priority PNs have the computational power of Turing machines. 5). 3 MODELING OF SOME CONCEPTS One of the key features of Petri nets is their capacity to graphically present certain relations and to visualize certain concepts. We shall give some examples of this below. 14a, we clearly see that after transition Tl has been fired and until transition T2 is fired, there are concurrent evolutions, from place Pl to place P3 on the one hand and from place P2 to place P4 on the other. Each of these two evolutions can be carried out at its own pace.

1. If there is a vertex m, = m, on the path from m 0 to m, (this latter not included), then m, has no successor. 2. If there is no vertex m7 = m, on the path from m 0 to m,, the root tree is extended by adding all the successors of m ; . For each successor m* of Hi;: 1) A component w of m, remains a component m for mk; 2) If there is a vertex m7 on the path from m 0 to mt such that mk ^ m J ? then a> is placed for each of the components greater than the components of m^. 18 Another example of a coverability root tree.

Indeed, m 0 —^J-» m,, and n^ — T ^ > mj. Transition T, is thus live. ^(mo) = {mo, m,, m 2 }. We may observe that there is no firing sequence which contains T, from m, (or from m2). That is to say that if marking n^ is reached, transition Tl will never be enabled again. This transition is not live. 4 A PN is live for an initial marking m 0 if all its transitions are live for m0. • In other words, if a PN is live, this means that, regardless of the evolution, no transition will become unfirable on a permanent basis.

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Discrete, Continuous, and Hybrid Petri Nets by Dr. René David, Pr. Hassane Alla (auth.)


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