基于单向耦合法的不确定复杂网络间有限时间同步

张檬; 韩敏

doi:10.16383/j.aas.c180102

基于单向耦合法的不确定复杂网络间有限时间同步

doi: 10.16383/j.aas.c180102

张檬^1,,
韩敏^2, ,

1.
沈阳航空航天大学自动化学院沈阳 110135
2.
大连理工大学电子信息与电气工程学部大连 116023

基金项目: 国家自然科学基金项目(61773087), 中央高校基本科研业务费专项资金(DUT20LAB114, DUT2018TB06), 沈阳航空航天大学引进人才科研启动基金(19YB70) 资助

详细信息

作者简介:
张檬：沈阳航空航天大学自动化学院讲师. 主要研究方向为复杂网络, 混沌控制与同步.E-mail: mengzhang@sau.edu.cn

韩敏：大连理工大学电子信息与电气工程学部教授. 主要研究方向为模式识别, 复杂系统建模与分析及时间序列预测. 本文通信作者.E-mail: minhan@dlut.edu.cn

计量
- 文章访问数: 53
- HTML全文浏览量: 16
- 被引次数: 0
出版历程
- 收稿日期: 2018-02-22
- 录用日期: 2018-05-07

Finite-time Synchronization Between Uncertain Complex Networks Based on Unidirectional Coupling Method

ZHANG Meng^1
,,
HAN Min^{2
, ,}

1.
School of Automation, Shenyang Aerospace University, Shenyang 110135
2.
Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116023

Funds: Supported by Special Fund for National Natural Science Foundation of China(61773087), the Special Funds for Fundamental Research Funds of the Central Universities (DUT20LAB114, DUT2018TB06), the Scientific Research Started Foundation for Introduced Talents of Shenyang Aerospace University (19YB70)

摘要

摘要: 针对具有不确定性的复杂网络有限时间同步问题, 提出一种新颖的单向耦合控制方法. 构建含有未知参量及未知拓扑结构的驱动- 响应复杂网络模型, 考虑两个网络具有不同的节点数, 同时受到时变耦合时滞的影响, 并且网络内部分别具有不同的节点系统. 基于有限时间稳定性理论和线性矩阵不等式变换, 通过在响应网络中引入单向耦合项, 实现两个网络间的有限时间同步, 同时准确辨识未知参量及未知拓扑结构. 仿真实验验证所提同步方法的有效性, 对比实验结果表明所提方法在减少耦合数量的同时具有更快的同步速率及更小的波动范围.
- 复杂网络 /
- 有限时间同步 /
- 单向耦合 /
- 未知参量
Abstract: To solve the problem of finite-time synchronization of uncertain complex networks, a novel unidirectional coupling control method is proposed. First, a drive-response complex network model with unknown parameters and unknown topological structure is constructed. The two networks have different sizes, and each of which contains two types of nonidentical nodes and time-varying coupling delay. Based on the finite-time stability theory and the linear matrix inequality, the finite-time synchronization between two networks is realized by adding a unidirectional coupling term in the response network, while the unknown parameters and the unknown topological structure can be identified, simultaneously. The simulation experiments verify the validity of the proposed scheme. Moreover, the comparison experiments show that the proposed method achieves faster synchronization rate and smaller fluctuation range as well as reduced coupling quantity.
- Complex networks /
- finite-time synchronization /
- unidirectional coupling /
- unknown parameter

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图 1 同步误差的演化 ${e_{i1}}(t),{e_{i2}}(t),{e_{i3}}(t)(i = 1,2, \cdots ,10)$

Fig. 1 Synchronous errors ${e_{i1}}(t),\;{e_{i2}}(t),\;{e_{i3}}(t)\left(i = 1,2, \cdots ,10\right)$

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图 2 未知参量的辨识 ${\hat a_{1i}}\left( {i = 1,2, \cdots ,5} \right)$

Fig. 2 Identification of the unknown parameters ${\hat a_{1i}}\left( {i = 1,2, \cdots ,5} \right)$

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图 3 未知参量的辨识 ${\hat d_{2i}}\left( {i = 6,7, \cdots ,10} \right)$

Fig. 3 Identification of the unknown parameters ${\hat d_{2i}}\left( {i = 6,7, \cdots ,10} \right)$

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图 4 未知拓扑结构的辨识 ${c_{ij}}$

Fig. 4 Identification of network structure ${c_{ij}}$

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图 5 未知拓扑结构的辨识 ${c_{ij}}$

Fig. 5 Identification of network structure ${c_{ij}}$

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图 6 未知拓扑结构的辨识 ${c_{ij}}$

Fig. 6 Identification of network structure ${c_{ij}}$

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图 7 未知拓扑结构的辨识 ${c_{ij}}$

Fig. 7 Identification of network structure ${c_{ij}}$

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图 8 本文方法与文献[14]定理1方法的平均误差曲线

Fig. 8 The average error of our method and Theorem 1 in [14]

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图 9 本文方法与文献[14]定理2方法的平均误差曲线

Fig. 9 The average error of our method and Theorem 2 in [14]

下载: 全尺寸图片幻灯片

表 1 本文方法与文献[14]定理1方法对比结果

Table 1 The comparison result between our method and the Theorem 1 in [14]

	同步时间Sync time	波动范围Fluctuation range
本文方法	0.657	[−4.5, 5.5]
文献[14]定理1	1.698	[−6.5, 7.4]

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表 2 本文方法与文献[14]中定理2方法对比结果

Table 2 The comparison result between our method and the Theorem 2 in [14]

	同步时间 Sync time	波动范围 Fluctuation range	耦合数量 Coupling number
本文方法	0.639	[−4.7, 6.9]	1
文献[14]定理2	1.095	[−9.5, 8,3]	2

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