| 引用本文: | 韩晓光,陈增强,刘忠信,张青.Petri网信标和陷阱计算的矩阵半张量积方法[J].控制理论与应用,2016,33(7):849~855.[点击复制] |
| HAN Xiao-guang,CHEN Zeng-qiang,LIU Zhong-xin,ZHANG Qing.Calculation of siphons and traps in Petri nets using semi-tensor product of matrices[J].Control Theory and Technology,2016,33(7):849~855.[点击复制] |
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| Petri网信标和陷阱计算的矩阵半张量积方法 |
| Calculation of siphons and traps in Petri nets using semi-tensor product of matrices |
| 摘要点击 3568 全文点击 2337 投稿时间：2015-11-17 修订日期：2016-08-03 |
| 查看全文 查看/发表评论 下载PDF阅读器 |
| DOI编号 10.7641/CTA.2016.50913 |
| 2016,33(7):849-855 |
| 中文关键词 Petri网 信标 陷阱 矩阵的半张量积 信标方程 陷阱方程 |
| 英文关键词 Petri nets (PNs) siphon trap the semi-tensor product (STP) of matrices siphon equation (SE) trap equation (TE) |
| 基金项目 国家自然科学基金项目(61573199, 61573200), 天津市自然科学基金项目(14JCYBJC18700, 13JCYBJC17400)资助. |
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| 中文摘要 |
| 本文基于矩阵半张量积(semi-tensor product, STP)方法研究了普通Petri网(Petri nets, PNs)信标和陷阱的计算
问题. 首先, 利用STP方法建立了两个矩阵方程, 分别称为Petri网的信标方程(siphon equation, SE)和陷阱方程(trap
equation, TE). 其次, 证明了计算Petri网的信标和陷阱分别等价于求信标方程(SE)和陷阱方程(TE)的非零解. 同时,
给出了计算Petri网所有信标和陷阱的算法. 最后, 实例和实验结果说明了本文方法的可行性与有效性. 本文所提出
的方法对于Petri网信标和陷阱的计算是非常有效的, 它只涉及到矩阵的乘法运算. |
| 英文摘要 |
| We address the problems of calculating siphons and traps in ordinary Petri nets (PNs) by resorting to the semi-tensor
product (STP) of matrices. First, two matrix equations, called the siphon equation (SE) and trap equation (TE), respectively, are
established by using STP. Second, it is proved that the problems of calculating all of the siphons and the traps in PNs are equivalent
to solve all nonzero solutions of SE and TE, respectively. An algorithm is proposed to calculate all siphons and traps in PNs. Finally,
an example and some experimental results are presented to illustrate the theoretical results and show that the proposed approach is
more effective than the existing approach in calculating all siphons and traps in PNs. The proposed approach only requires matrix
manipulations. |
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