引用本文:李绍勇,肖兴达,蔡颖,厚彩琴,韩喜莲,马兵善.普通Petri网最大可达数的两段式死锁控制策略[J].控制理论与应用,2017,34(2):243~250.[点击复制]
LI Shao-yong,XIAO Xing-da,CAI Ying,HOU Cai-qin,HAN Xi-lian,MA Bing-shan.A two-stage deadlock control policy with maximally reachable number for ordinary Petri nets[J].Control Theory and Technology,2017,34(2):243~250.[点击复制]
普通Petri网最大可达数的两段式死锁控制策略
A two-stage deadlock control policy with maximally reachable number for ordinary Petri nets
摘要点击 2615  全文点击 2006  投稿时间：2016-01-27  修订日期：2017-01-15
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DOI编号  10.7641/CTA.2017.60064
  2017,34(2):243-250
中文关键词  Petri网  死锁控制  基本信标  最大可达数  最大许可行为数目
英文关键词  Petri nets  deadlock control  elementary siphon (ES)  maximally reachable number (MRN)  number of maximally permissive behavior (NMPB)
基金项目  国家自然科学基金(61364004）
作者单位E-mail
李绍勇* 兰州理工大学 lishaoyong99@163.com 
肖兴达 开封大学电子电气工程学院  
蔡颖 兰州理工大学土木工程学院  
厚彩琴 兰州理工大学土木工程学院  
韩喜莲 兰州理工大学土木工程学院  
马兵善 兰州理工大学土木工程学院  
中文摘要
      针对普通Petri网的死锁问题, 本文提出了可实现最大可达数的两段式死锁控制策略(deadlock control policy, DCP). 第一步, 该策略求解原网(N0, M0)的基本信标(elementary siphons, ES)和从属信标(dependent siphons, DS), 对每个基本信标添加控制库所(control place, CP)和控制变迁(control transition, CT), 获得拓展网系统(N′, M′). 第二步, 构建拓展网系统的P -不变式整数规划问题, 测试原网中从属信标的可控性. 若所有从属信标满足可控条件, 则直接得到活性受控网系统(N*, M*); 反之, 对不满足可控条件的从属信标也添加控制库所和变迁, 从而也得到了(N*, M*). 通过理论分析和算例验证, 表明了该死锁控制策略的正确性和有效性. 相比目前文献中的可实现最大许可行为数目(number of maximally permissive behavior, NMPB)的死锁预防策略, 该DCP获取的活性受控网系统(N?, M?)可达数目与原网(N0, M0)是相同的, 且最大可达数(maximally reachable number, MRN)高于最大许可行为数目NMPB.
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 policy. 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.