Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy

doi:10.1007/s10483-018-2304-9

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (3): 353-364.doi: https://doi.org/10.1007/s10483-018-2304-9

Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy

Lin DU, Yong YANG, Youming LEI

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2017-06-30 修回日期:2017-08-08 出版日期:2018-03-01 发布日期:2018-03-01
通讯作者: Youming LEI E-mail:leiyouming@nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11672231 and 11672233), the Natural Science Foundation of Shaanxi Province (No. 2016JM1010), the Fundamental Research Funds for the Central Universities (No. 3102017AX008), and the Seed Foundation of Innovation and Creation for Graduate Students at the Northwestern Polytechnical University of China (No. Z2017187)

Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy

Lin DU, Yong YANG, Youming LEI

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2017-06-30 Revised:2017-08-08 Online:2018-03-01 Published:2018-03-01
Contact: Youming LEI E-mail:leiyouming@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11672231 and 11672233), the Natural Science Foundation of Shaanxi Province (No. 2016JM1010), the Fundamental Research Funds for the Central Universities (No. 3102017AX008), and the Seed Foundation of Innovation and Creation for Graduate Students at the Northwestern Polytechnical University of China (No. Z2017187)

摘要/Abstract

摘要：

This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this paper shows that tracking errors of all nodes in a fractional-order complex network converge to zero. This simple yet practical scheme can be used in many networks such as small-world networks and scale-free networks. Unlike the existing methods which assume the coupling configuration among the nodes of the network with diffusivity, symmetry, balance, or irreducibility, in this case, these assumptions are unnecessary, and the proposed adaptive strategy is more feasible. Two examples are presented to illustrate effectiveness of the proposed method.

关键词: SH-waves, anisotropic media, non-circular cavity surfaced with lining, fractional-order chaotic system, adaptive control, complex dynamic network, synchronization

Abstract:

Key words: adaptive control, synchronization, SH-waves, anisotropic media, non-circular cavity surfaced with lining, complex dynamic network, fractional-order chaotic system

中图分类号:

93C83
93D05

Lin DU, Yong YANG, Youming LEI. Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(3): 353-364.

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Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy

Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy

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