Supervisor synthesis for Petri nets with unobservable and uncontrollable transitions

doi:10.3969/j.issn.1000-1565.2023.05.011

Abstract

Abstract: A controller synthesis method based on integer linear programming is proposed to solve the forbidden state problem of discrete event systems with both unobservable and uncontrollable events. Firstly, according to the structural characteristics of Petri net, a set of linear constraints for all unobservable transitions and uncontrollable transitions are constructed, and the given constraints were abstracted into integer linear programming problems. Secondly, the allowable linear constraint is obtained by resolving the integer linear programming problem. Finally, the controller is designed based on library invariants and the transformed allowable linear constraints are integrated into Petri net. The simulation- DOI:10.3969/j.issn.1000-1565.2023.05.011含不可观和不可控变迁Petri网的控制器综合方法郝晋渊¹,高丽敏²,冉宁^2,3,黄淼²,郝真鸣^3,4(1.河北大学-中央兰开夏传媒与创意学院,河北保定 071002;2.河北大学电子信息工程学院节能技术研发中心,河北保定 071002;3.河北大学电子信息工程学院,河北保定 071002;4.河北大学电子信息工程学院物联网智能技术研究中心,河北保定 071002)摘要:针对同时含有不可观和不可控事件的离散事件系统禁止状态问题,提出了一种基于整数线性规划的控制器综合方法.首先,依据Petri网的结构特性构建所有不可观变迁及不可控变迁需满足的线性约束条件集合,将给定约束条件抽象为整数线性规划问题.其次,通过求解整数线性规划问题得到允许线性约束.最后,基于库所不变量的方法设计控制器并将转换后的允许线性约束综合到Petri网中.实验仿真表明提出的方法简单高效,能够保障系统不进入禁止状态,对离散事件系统监控问题具有理论指导意义.关键词:Petri网;禁止状态;约束转换;整数线性规划中图分类号:TP11 文献标志码:A 文章编号:1000-1565(2023)05-0517-08Supervisor synthesis for Petri nets with unobservable and uncontrollable transitionsHAO Jinyuan¹,GAO Limin²,RAN Ning^2,3,HUANG Miao²,HAO Zhenming^3,4(1. HBU-UCLAN School of Media, Communication and Creative Industries, Hebei University, Baoding 071002,China;2. Lab of Energy-Saving Technology, College of Electronic Informational Engineering, Hebei University, Baoding 071002, China; 3. College of Electronic Informational Engineering, Hebei University, Baoding 071002,China; 4. Laboratory of IoT Technology, College of Electronic Informational Engineering, Hebei University, Baoding 071002, China)Abstract: A controller synthesis method based on integer linear programming is proposed to solve the forbidden state problem of discrete event systems with both unobservable and uncontrollable events. Firstly, according to the structural characteristics of Petri net, a set of linear constraints for all unobservable transitions and uncontrollable transitions are constructed, and the given constraints were abstracted into integer linear programming problems. Secondly, the allowable linear constraint is obtained by resolving the integer linear programming problem. Finally, the controller is designed based on library invariants and the transformed allowable linear constraints are integrated into Petri net. The simulation- 收稿日期:2022-03-02 基金项目:国家自然科学基金资助项目(62373132);教育部“春晖计划”合作科研项目(HZKY20220257);中央引导地方科技发展基金资助项目(236Z1602G);河北省高等学校科学技术研究项目(BJ2021008);河北省引进留学人员资助项目(C20190319);河北大学"一省一校"专项基金资助项目(801260201137) 第一作者:郝晋渊(1990—),女,河北保定人,河北大学讲师,主要从事人工智能、信息技术、新媒体传播等研究.E-mail:hjy@hbu.edu.cn 通信作者:冉宁(1978—),男,河北丰宁人,河北大学副教授,主要从事离散事件系统、监控理论等研究.E-mail:ranning87@hotmail.com第5期郝晋渊等:含不可观和不可控变迁Petri网的控制器综合方法results indicate that the suggested technique is uncomplicated and efficient, and can ensure that the system does not enter forbidden state, which has theoretical guiding significance for discrete event system monitoring.

Key words: Petri net, forbidden state, constraint transformation, integer linear programming

CLC Number:

TP11

HAO Jinyuan,GAO Limin,RAN Ning,HUANG Miao,HAO Zhenming. Supervisor synthesis for Petri nets with unobservable and uncontrollable transitions[J]. Journal of Hebei University(Natural Science Edition), 2023, 43(5): 517-524.

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