• 开发研究与工程应用 •

### 标注Petri网中的最小初始标识估计

1. 1. 青岛大学 自动化学院, 山东 青岛 266071;
2. 青岛大学 复杂性科学研究所, 山东 青岛 266071
• 收稿日期:2020-02-26 修回日期:2020-04-28 发布日期:2020-05-11
• 作者简介:徐淑琳(1995-),女,硕士研究生,主研方向为离散事件系统;周广瑞,硕士研究生;岳昊(通信作者),副教授、博士。
• 基金资助:
国家自然科学基金（61402216，61673228）。

### Estimation of Minimum Initial Marking in Labeled Petri Nets

XU Shulin1, ZHOU Guangrui1, YUE Hao1,2

1. 1. School of Automation, Qingdao University, Qingdao, Shandong 266071, China;
2. Institute of Complexity Science, Qingdao University, Qingdao, Shandong 266071, China
• Received:2020-02-26 Revised:2020-04-28 Published:2020-05-11

Abstract: In order to obtain the minimum resources required for initialization of manufacturing systems and realize the optimal resource allocation, these systems are modeled by labeled Petri nets, and this paper offers the study of the estimation problem of the minimum initial marking in labeled Petri nets. Given a labeled Petri net, a new algorithm for estimating the minimum initial marking is proposed based on dynamic programming when the unobservable transitions form an acyclic subnet. After a given sequence of labels is observed, the limit of the number of unobservable transitions is relaxed, and the schematic diagram of node evolution is constructed according to the proposed algorithm. When the same firing vector appears, only the current minimal initial marking estimation is retained, and the total number of tokens of the minimal initial marking estimation is compared based on the process of node evolution. An example of the labeled Petri net model of the manufacturing system is given to test the effectiveness of the algorithm. The minimum initial marking is[1000]T, and the corresponding transition sequence is t1t3t4t6,which meets the structural requirements of the given labeled Petri nets. Compared with the existing algorithm using dynamic programming, the proposed algorithm can obtain the minimum initial marking estimatation with a smaller total number of tokens.