Chaotic synchronization based on nonlinear state-observer and its application in secure communication

Abstract

Chaotic synchronization is a branch of chaotic control. Nowadays, the research and application of chaotic synchronization have become a hot topic and one of the development directions is for the research on chaos. In this paper, a universal nonlinear state-observer is presented for a class of universal chaotic systems to realize the chaotic synchronization, according to the theory of state-observer in the modern control theory. And theoretic analysis and simulation results have illustrated the validity of the approach. Moreover, the approach of synchronization proposed in this paper is very easy, flexible and universal with high synchronization precision. When the approach is applied to secure communication, the results are satisfying.

Keywords

chaotic synchronization / nonlinear state-observer / synchronization error / secure communication

References

[1] Wu C W, Chua L O. Unified framework for synchronization and control of dynamical system [J]. Int J Bifurc Chaos, 1994, 4(4): 979-998

[2] Grassi G, Mascolo S. Nonlinear observer design to synchronize hyper-chaotic systems via a scalar signal [J]. IEEE Trans on Circuits and syst, 1997, 44(10): 1011-1014

[3] Di Bernrdo M. An Adaptive Approach to the Control and Synchronization of continuous time chaotic System[J]. M J Bifurc Chaos, 1996, 6: 557-557

[4] Yao Lina. The research of the control and synchronization of chaotic systems based on nonlinear state-observer [D]. 2002, Zhengzhou: Zhengzhou University

[5] WANG Futian, HONG Yiguang. On robust and adaptive synchronization of chaotic system [J]. Control theory and application, 2000:34–36 (in Chinese).

[6] Guan Xinping, He Yanhui. Synchronization of a class of chaotic systems in the presence of perturbation by an observer [J]. Physics Transaction, 2003, 52(2): 276-280 (in Chinese)

[7] Yang Luxi, Li Ke. The stabilization analysis of nonlinear observer for the chaotic synchronization [J]. Chinese Science, 2001, 31: 355-362 (in Chinese)

[8] Li Ke, Liu Ju. Disperse synchronization of chaos based on nonlinear observer [J]. Automation transaction, 2001, 27: 280-283 (in Chinese)

[9] Moez F. Observer-based exact synchronization of ideal and mismatched chaotic systems [J]. Physics Letters (A Volume), 2003, 309: 53-60

[10] Ercan S, Omer M, Umut E. Observer-based control of a class of chaotic systems [J]. Physics Letters (A Volume), 2001, 279: 47-55

[11] Chen Qizong. Theory and design of linear system[M]. 1988, Beijing: Science Publishing House