TY - JOUR
T1 - Controllability conditions of resultant siphons in a class of Petri nets
AU - Wang, Shou Guang
AU - Wang, Cheng Ying
AU - Zhou, Meng Chu
N1 - Funding Information:
Manuscript received January 15, 2011; revised June 8, 2011; accepted August 6, 2011. Date of publication November 10, 2011; date of current version August 15, 2012. This work was supported in part by the National Natural Science Foundation of China under Grants 61100056 and 61034004, by the Zhejiang Provincial Natural Science Foundation of China under Grants Y1090232 and Y1100830, by the Science Fund for Young Scholars of Zhejiang Gongshang University, and by the Zhejiang Provincial Education Department Foundation under Grant Y201018216. This paper was recommended by Associate Editor A. Konar.
PY - 2012
Y1 - 2012
N2 - Strict minimal siphons (SMSs) play a key role in the development of deadlock prevention policies by using Petri nets for flexible manufacturing systems (FMSs). In this paper, given two SMSs and their resultant siphon, the concept of key resource subsets is proposed which is shown to be the critical factor in deciding the controllability conditions of the latter. A necessary and sufficient condition is then proposed under which the resultant siphon can be always marked if its two SMSs are M-controlled, i.e., invariant controlled via the method proposed by Moody and Antsaklis. As for a resultant siphon that is composed by more than two composable SMSs, a sufficient condition is proposed under which it can be always marked if its SMSs are M-controlled. They are established by analyzing the structural characteristics and markings of the resource subnets in a class of Petri nets called L-S 3PR. When they are applied to some classes of S 3PR nets, i.e., those whose controlled ones are maximally permissive and live once their original SMSs are M-controlled, the number of monitors may be reduced. An FMS example is used to illustrate the application of the results.
AB - Strict minimal siphons (SMSs) play a key role in the development of deadlock prevention policies by using Petri nets for flexible manufacturing systems (FMSs). In this paper, given two SMSs and their resultant siphon, the concept of key resource subsets is proposed which is shown to be the critical factor in deciding the controllability conditions of the latter. A necessary and sufficient condition is then proposed under which the resultant siphon can be always marked if its two SMSs are M-controlled, i.e., invariant controlled via the method proposed by Moody and Antsaklis. As for a resultant siphon that is composed by more than two composable SMSs, a sufficient condition is proposed under which it can be always marked if its SMSs are M-controlled. They are established by analyzing the structural characteristics and markings of the resource subnets in a class of Petri nets called L-S 3PR. When they are applied to some classes of S 3PR nets, i.e., those whose controlled ones are maximally permissive and live once their original SMSs are M-controlled, the number of monitors may be reduced. An FMS example is used to illustrate the application of the results.
KW - Automated manufacturing systems
KW - Petri nets
KW - deadlock
KW - discrete event systems (DES)
KW - siphon
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U2 - 10.1109/TSMCA.2011.2170419
DO - 10.1109/TSMCA.2011.2170419
M3 - Article
AN - SCOPUS:84865435926
SN - 1083-4427
VL - 42
SP - 1206
EP - 1215
JO - IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans
JF - IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans
IS - 5
M1 - 6075272
ER -