Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

doi:10.1088/1674-1056/21/6/060507

中国物理B ›› 2012, Vol. 21 ›› Issue (6): 60507-060507.doi: 10.1088/1674-1056/21/6/060507

Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control

付士慧^a, 陆启韶^b, 杜莹^c

a. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China;
b. School of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
c. School of Science, East China University of Science and Technology, Shanghai 200237, China

收稿日期:2012-01-16 修回日期:2012-02-17 出版日期:2012-05-01 发布日期:2012-05-01

Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control

Fu Shi-Hui(付士慧)^a)†, Lu Qi-Shao(陆启韶)^b), and Du Ying(杜莹)^c)

a. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China;
b. School of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
c. School of Science, East China University of Science and Technology, Shanghai 200237, China

Received:2012-01-16 Revised:2012-02-17 Online:2012-05-01 Published:2012-05-01
Contact: Fu Shi-Hui E-mail:fshtp@163.om

摘要/Abstract

摘要： Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lyapunov's stability theory, linear and nonlinear feedback control of adaptive H_∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H_∞-norm constraint. Adaptive H_∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.

关键词: chaotic system, H_∞ synchronization, generalized Hamiltonian system, Lyapunov's stability theory, adaptive synchronization, Lorenz system, Chen system

Abstract: Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lyapunov's stability theory, linear and nonlinear feedback control of adaptive H_∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H_∞-norm constraint. Adaptive H_∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.

Key words: chaotic system, H_∞ synchronization, generalized Hamiltonian system, Lyapunov's stability theory, adaptive synchronization, Lorenz system, Chen system

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

05.45.Gg (Control of chaos, applications of chaos) 05.45.-a (Nonlinear dynamics and chaos)

付士慧, 陆启韶, 杜莹. Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control[J]. 中国物理B, 2012, 21(6): 60507-060507.

Fu Shi-Hui(付士慧), Lu Qi-Shao(陆启韶), and Du Ying(杜莹) . Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control[J]. Chin. Phys. B, 2012, 21(6): 60507-060507.

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Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control

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