A two-stage deadlock control policy with maximally reachable number for ordinary Petri nets

doi:10.7641/CTA.2017.60064

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	A two-stage deadlock control policy with maximally reachable number for ordinary Petri nets
	Li, Shao-Yong 2; Xiao, Xing-Da 1; Cai, Ying 2; Hou, Cai-Qin 2; Han, Xi-Lian 2; Ma, Bing-Shan 2
刊名	Kongzhi Lilun Yu Yingyong/Control Theory and Applications
	2017-02-01
卷号	34 期号:2 页码:243-250
关键词	Controllability Integer programming Petri nets Deadlock control Deadlock control policy Deadlock prevention policy Elementary siphon Integer programming problems Maximally reachable number (MRN) Number of maximally permissive behavior (NMPB) Ordinary Petri net
ISSN号	10008152
DOI	10.7641/CTA.2017.60064
英文摘要	This paper develops a two-stage deadlock control policy (DCP) with maximally reachable number (MRN) for the deadlock problems in ordinary Petri nets (OPNs). First, this DCP solves elementary siphons (ESs) and dependent siphons (DSs) in the original uncontrolled net (N0;M0) and then adds a control place (CP) and a control transition (CT) for each ES. Accordingly, an extended net system (N';M') is obtained. Second, the controllability test for DSs in N0 is executed by means of constructing an integer programming problem (IPP) of P-invariants of N'. If all DSs meet the controllability, then a live controlled system (N;M) is achieved directly, implying that the extended net system (N';M') is live. Conversely, the corresponding CPs and CTs are added for those DSs that cannot meet the controllability. Therefore, the live controlled system (N;M) can be obtained as well. Theoretical analysis and examples show the correctness and efficiency of the proposed DCP. Compared with the relevant deadlock prevention policies with number of maximally permissive behavior (NMPB) in the existing literature for OPNs, the reachable number of the live controlled system (N;M) obtained by the proposed DCP is the same as that of the original uncontrolled net (N0;M0), i. e., maximally reachable number (MRN) is greater than NMPB. ©2017, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.
语种	中文
出版者	South China University of Technology
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/114571]
专题	土木工程学院
作者单位	1.School of Electronic and Electrical Engineering, Kaifeng University, Kaifeng; Henan; 475004, China 2.School of Civil Engineering, Lanzhou University of Technology, Lanzhou; Gansu; 730050, China;
推荐引用方式 GB/T 7714	Li, Shao-Yong,Xiao, Xing-Da,Cai, Ying,et al. A two-stage deadlock control policy with maximally reachable number for ordinary Petri nets[J]. Kongzhi Lilun Yu Yingyong/Control Theory and Applications,2017,34(2):243-250.
APA	Li, Shao-Yong,Xiao, Xing-Da,Cai, Ying,Hou, Cai-Qin,Han, Xi-Lian,&Ma, Bing-Shan.(2017).A two-stage deadlock control policy with maximally reachable number for ordinary Petri nets.Kongzhi Lilun Yu Yingyong/Control Theory and Applications,34(2),243-250.
MLA	Li, Shao-Yong,et al."A two-stage deadlock control policy with maximally reachable number for ordinary Petri nets".Kongzhi Lilun Yu Yingyong/Control Theory and Applications 34.2(2017):243-250.