第13卷第5期 智能系统学报 Vol.13 No.5 2018年10月 CAAI Transactions on Intelligent Systems Oct.2018 D0:10.11992/tis.201704023 网络出版地址：http:/kns.cnki.net/kcms/detail/23.1538.TP.20180425.0911.002.html 非线性布尔网络系统模糊建模与动态性能分析 吕红丽'，宋玉晶'，段培永2 (1.山东建筑大学信息与电气工程学院，山东济南250101；2.山东师范大学信息科学与工程学院，山东济南 250014) 摘要：针对非线性系统难以精确建模与动态性能分析的基本控制问题，基于模糊动态模型把布尔网络系统理 论推广到非线性布尔网络系统，建立了模糊动态布尔网络控制系统的模型。引入模糊动态模型，对非线性布尔 网络进行模糊建模，分别建立了非线性布尔网络系统的局部模型和全局模型。从系统的局部意义和全局意义 上，对系统进行了能控性、能观性、稳定性等动态性能分析。最后，以多输入多输出的非线性布尔网络系统实 例为具体研究对象，建立了系统的局部模型和全局模型，并对动态性能进行了仿真分析，得到了实验结果。实 验结果表明，模糊动态布尔网络控制系统对非线性布尔网络系统的建模是有效的，动态性能分析是合理的，对 模糊动态布尔网络控制系统的进一步分析有重要意义。 关键词：模糊动态模型；布尔网络：半张量积：局部模型；全局模型；能控性：能观性：稳定性 中图分类号：TP273文献标志码：A文章编号：1673-4785(2018)05-0707-09 中文引用格式：吕红丽，宋玉晶，段培永.非线性布尔网络系统模糊建模与动态性能分析J.智能系统学报，2018,13(5)： 707-715. 英文引用格式：LYU Hongli,,SONGYujing,.DUAN Peiyong..Fuz四y modeling and dynamic analysis of nonlinear Boolean networks systems[J].CAAI transactions on intelligent systems,2018,13(5):707-715. Fuzzy modeling and dynamic analysis of nonlinear Boolean networks systems LYU Hongli',SONG Yujing',DUAN Peiyong? (1.School of Information and Electrical Engineering,Shandong Jianzhu University,Ji'nan 250101,China;2.School of Information Science and Engineering,Shandong Normal University,Ji'nan 250014,China) Abstract:Considering the difficulty in accurately modeling nonlinear systems and analyzing their dynamic properties, the Boolean network system theories are extended to the nonlinear Boolean network system based on a fuzzy dynamic model,establishing a model of fuzzy dynamic Boolean network control systems.The fuzzy dynamic model is intro- duced to build a fuzzy model of nonlinear Boolean network,establishing the local and global models of the nonlinear Boolean network systems.The dynamic properties,which include controllability,observability,and stability of the sys- tem,are analyzed from the local and global meanings of the system.Finally,a multi-input multi-output nonlinear Boolean network system is taken as a numerical example,and the local and global models of the system are established. The dynamic properties are simulated and analyzed,and the experimental results are obtained.The results show that the fuzzy dynamic Boolean network control system is effective in modeling nonlinear Boolean network systems and reason- ably analyzes the dynamic properties,which is of great significance for further analysis of the fuzzy dynamic Boolean network control systems. Keywords:fuzzy dynamical model;Boolean network;semi-tensor product;local model;global model;controllability; observability:stability 收稿日期：2017-04-19.网络出版日期：2018-04-25 1965年，Zadeh首次提出基于模糊集合的模 基金项目：国家自然科学基金项目(61374187,61403237) 通信作者：宋玉品.E-mail:xiaosongyj(@qq.com. 糊数学概念。1974年，Mamdani首先将模糊数学DOI: 10.11992/tis.201704023 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.TP.20180425.0911.002.html 非线性布尔网络系统模糊建模与动态性能分析 吕红丽1 ，宋玉晶1 ，段培永2 （1. 山东建筑大学 信息与电气工程学院，山东 济南 250101; 2. 山东师范大学 信息科学与工程学院，山东 济南 250014） 摘 要：针对非线性系统难以精确建模与动态性能分析的基本控制问题，基于模糊动态模型把布尔网络系统理 论推广到非线性布尔网络系统，建立了模糊动态布尔网络控制系统的模型。引入模糊动态模型，对非线性布尔 网络进行模糊建模，分别建立了非线性布尔网络系统的局部模型和全局模型。从系统的局部意义和全局意义 上，对系统进行了能控性、能观性、稳定性等动态性能分析。最后，以多输入多输出的非线性布尔网络系统实 例为具体研究对象，建立了系统的局部模型和全局模型，并对动态性能进行了仿真分析，得到了实验结果。实 验结果表明，模糊动态布尔网络控制系统对非线性布尔网络系统的建模是有效的，动态性能分析是合理的，对 模糊动态布尔网络控制系统的进一步分析有重要意义。 关键词：模糊动态模型；布尔网络；半张量积；局部模型；全局模型；能控性；能观性；稳定性 中图分类号：TP273 文献标志码：A 文章编号：1673−4785(2018)05−0707−09 中文引用格式：吕红丽, 宋玉晶, 段培永. 非线性布尔网络系统模糊建模与动态性能分析[J]. 智能系统学报, 2018, 13(5): 707–715. 英文引用格式：LYU Hongli, SONG Yujing, DUAN Peiyong. Fuzzy modeling and dynamic analysis of nonlinear Boolean networks systems[J]. CAAI transactions on intelligent systems, 2018, 13(5): 707–715. Fuzzy modeling and dynamic analysis of nonlinear Boolean networks systems LYU Hongli1 ，SONG Yujing1 ，DUAN Peiyong2 (1. School of Information and Electrical Engineering, Shandong Jianzhu University, Ji’nan 250101, China; 2. School of Information Science and Engineering, Shandong Normal University, Ji’nan 250014, China) Abstract: Considering the difficulty in accurately modeling nonlinear systems and analyzing their dynamic properties, the Boolean network system theories are extended to the nonlinear Boolean network system based on a fuzzy dynamic model, establishing a model of fuzzy dynamic Boolean network control systems. The fuzzy dynamic model is intro￾duced to build a fuzzy model of nonlinear Boolean network, establishing the local and global models of the nonlinear Boolean network systems. The dynamic properties, which include controllability, observability, and stability of the sys￾tem, are analyzed from the local and global meanings of the system. Finally, a multi-input multi-output nonlinear Boolean network system is taken as a numerical example, and the local and global models of the system are established. The dynamic properties are simulated and analyzed, and the experimental results are obtained. The results show that the fuzzy dynamic Boolean network control system is effective in modeling nonlinear Boolean network systems and reason￾ably analyzes the dynamic properties, which is of great significance for further analysis of the fuzzy dynamic Boolean network control systems. Keywords: fuzzy dynamical model; Boolean network; semi-tensor product; local model; global model; controllability; observability; stability 1965 年，Zadeh[1]首次提出基于模糊集合的模 糊数学概念。1974 年，Mamdani[2]首先将模糊数学 收稿日期：2017−04−19. 网络出版日期：2018−04−25. 基金项目：国家自然科学基金项目 (61374187, 61403237). 通信作者：宋玉晶. E-mail：xiaosongyj@qq.com. 第 13 卷第 5 期 智 能 系 统 学 报 Vol.13 No.5 2018 年 10 月 CAAI Transactions on Intelligent Systems Oct. 2018