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Extended Elementary Siphons and Their Application to Liveness‐Enforcement of Generalized P etri Nets
Author(s) -
Hou YiFan,
Li ZhiWu,
AlAhmari Abdulrahman M.,
ElTamimi AbdulAziz Mohammed,
Nasr Emad Abouel
Publication year - 2014
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.801
Subject(s) - controllability , liveness , petri net , siphon (mollusc) , supervisor , set (abstract data type) , class (philosophy) , computer science , mathematical optimization , mathematics , theoretical computer science , distributed computing , artificial intelligence , programming language , biology , ecology , political science , law
As a significant structural object, siphons are extensively employed to implement a large number of deadlock prevention and liveness‐enforcing methods for flexible manufacturing systems modeled by P etri nets. By linear combinations, a set of elementary siphons is chosen from all strict minimal ones to be controlled and thus the structural complexity of a supervisor is greatly reduced. The concept of elementary siphons is originally proposed for ordinary P etri nets. When applied to generalized Petri nets, their selection and controllability require an additional study. In this work, the concept of augmented siphons is proposed to extend the application of the elementary ones to a class of generalized P etri nets, GLS 3 PR . Based on graph theory, a siphon extraction algorithm is developed to obtain all strict minimal siphons, from which augmented elementary ones are computed. In addition, the controllability conditions of dependent siphons are developed. Through fully investigating the net structure, especially weight information, the set of augmented elementary siphons is more compact and well suits for generalized P etri net models under consideration. Some examples are used to illustrate the proposed method.