A novel adaptive-impulsive synchronization of fractional-order chaotic systems

doi:10.1088/1674-1056/24/10/100502

中国物理B ›› 2015, Vol. 24 ›› Issue (10): 100502-100502.doi: 10.1088/1674-1056/24/10/100502

A novel adaptive-impulsive synchronization of fractional-order chaotic systems

Leung Y. T. Andrew^a, Li Xian-Feng^a, Chu Yan-Dong^b, Zhang Hui^c

a Department of Architecture and Civil Engineering, City University of Hong Kong, China;
b School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China;
c School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

收稿日期:2015-03-02 修回日期:2015-05-18 出版日期:2015-10-05 发布日期:2015-10-05
基金资助:
Project supported by the National Natural Science Foundations of China (Grant Nos. 11161027 and 11262009), the Key Natural Science Foundation of Gansu Province, China (Grant No. 1104WCGA195), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20136204110001).

A novel adaptive-impulsive synchronization of fractional-order chaotic systems

Leung Y. T. Andrew^a, Li Xian-Feng^a, Chu Yan-Dong^b, Zhang Hui^c

a Department of Architecture and Civil Engineering, City University of Hong Kong, China;
b School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China;
c School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

Received:2015-03-02 Revised:2015-05-18 Online:2015-10-05 Published:2015-10-05
Contact: Leung Y. T. Andrew E-mail:aytleung@gmail.com
Supported by:
Project supported by the National Natural Science Foundations of China (Grant Nos. 11161027 and 11262009), the Key Natural Science Foundation of Gansu Province, China (Grant No. 1104WCGA195), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20136204110001).

摘要/Abstract

摘要： A novel adaptive-impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors' bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive-impulsive control scheme.

关键词: adaptive-impulsive synchronization, fractional order, chaotic systems, combined feedback strength

Abstract: A novel adaptive-impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors' bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive-impulsive control scheme.

Key words: adaptive-impulsive synchronization, fractional order, chaotic systems, combined feedback strength

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

05.45.Gg (Control of chaos, applications of chaos)

Leung Y. T. Andrew, Li Xian-Feng, Chu Yan-Dong, Zhang Hui. A novel adaptive-impulsive synchronization of fractional-order chaotic systems[J]. 中国物理B, 2015, 24(10): 100502-100502.

Leung Y. T. Andrew, Li Xian-Feng, Chu Yan-Dong, Zhang Hui. A novel adaptive-impulsive synchronization of fractional-order chaotic systems[J]. Chin. Phys. B, 2015, 24(10): 100502-100502.

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A novel adaptive-impulsive synchronization of fractional-order chaotic systems

A novel adaptive-impulsive synchronization of fractional-order chaotic systems

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