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Synchronization of the fractional-order generalized augmented Lii system and its circuit implementation

ISSN号：1674-1056
期刊名称：《中国物理B：英文版》
时间：0
分类：TP273[自动化与计算机技术—控制科学与工程;自动化与计算机技术—检测技术与自动化装置] TN911.1[电子电信—通信与信息系统;电子电信—信息与通信工程]
作者机构：[1]Department of Automation, Tianjin University of Science and Technology, Tianjin 300222, China, [2]Department of Industry Design, Tianjin University of Science and Technology, Tianjin 300222, China
相关基金：Project supported by the National Natural Science Foundation of China （Grant No. 61174094） and the Young Scientists Fund of the National Natural Science Foundation of China （Grant No. 11202148）.

关键词： LTI系统, 分数阶系统, 同步性, 电路实现, LYAPUNOV指数谱, 广义, 线性反馈控制器, 混沌吸引子, fractional-order generalized augmented Lii system, nonlinear feedback synchronization, numericalsimulation, circuit design

中文摘要：

In this paper, the synchronization of the fractional-order generalized augmented Lu¨ system is investigated. Based on the predictor–corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincare′maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system parameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchronization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses,which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.

英文摘要：

In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincar6 maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system pa- rameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchro- nization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.

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