基于高增益降维观测器的一类混沌同步

韩冬; 朱芳来

doi:10.7498/aps.62.120513

摘要

针对一类混沌系统, 当不满足观测器匹配条件时, 讨论了基于观测器的混沌同步及保密通讯问题.通过设计辅助驱动信号, 使得观测器匹配条件得以满足.为了处理辅助驱动信号中的未知变量, 使用高增益观测器作为近似微分器, 不仅给出了辅助驱动信号的估计值, 还给出了辅助驱动信号的微分估计值.基于辅助驱动信号的估计值, 提出了一种能与非线性项和干扰影响解耦的降维观测器作为响应系统, 达到了与驱动系统的同步.在同步的基础上, 再基于辅助驱动信号及其微分的估计值, 提出了一种保密信息还原的方法.最后, 针对Rössler系统进行仿真, 仿真结果表明所提出的方法是有效的.

关键词:

Abstract

In this paper we consider the issues of chaos synchronization and chaos-based secure communication when the so-called observer matching condition is not satisfied. An auxiliary drive signal vector is introduced such that the observer matching condition is satisfied. High-gain observers are employed to estimate the auxiliary drive signals as well as their derivatives in a finite time by using the drive signals of original system. Then, a kind of reduced-order observer is constructed which can directly eliminate the influence of the non-linear part and the disturbances of the system. Based on the estimates of states as well as the estimates of the auxiliary signals and their derivatives, a kind of message information recovery method is proposed. Finally, the Rössler chaotic system is used as a simulation example to verify the effectiveness of the proposed method.

Keywords:

作者及机构信息

韩冬,
朱芳来

1.
同济大学电子与信息工程学院, 上海 200092

基金项目: 国家自然科学基金 (批准号: 61074009)、高等学校博士学科点专项科研基金 (批准号: 20110072110015)、广西制造系统与先进制造技术重点实验室 (批准号: PF110289)和上海市重点学科项目(批准号: B004)资助的课题.

Authors and contacts

1.
College of Electronics and Information, Tongji University, Shanghai 200092, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61074009), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110072110015), the Guangxi Key Laboratory of Manufacturing System and Advanced Manufacturing Technology, China (Grant No. PF110289), and the Shanghai Leading Academic Discipline Project, China (Grant No. B004).

参考文献

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[3]	Ji D H, Jeong S C, Park J H, Won S C 2012 Nonlinear Dyn. 69 1125
[4]	Zhang L W, Liao T L, Hou Y Y, Yan J J 2012 Int. J. Bifurcat. Chaos 22 1250058
[5]	Zhang Z Q, Shao H Y, Wang Z, Shen H 2012 Appl. Math. Comput. 218 7614
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[7]	Zhu F L, Xu J, Chen M Y 2012 IEEE Circuits-I 59 2702
[8]	Gao T G, Chen Z Q, Yuan Z Z, Gu Q L 2004 Acta Phys. Sin. 53 1305 (in Chinese) [高铁杠, 陈增强, 袁著祉, 顾巧论 2004 53 1305]
[9]	Chen M, Zhou D, Shang Y 2005 Chaos, Soliton. Fract. 25 573
[10]	Bowong S, Kakmeni F M M, Fotsin H 2006 Phys. Lett. A 355 193
[11]	Zhu F L 2009 Chaos, Soliton. Fract. 40 2384
[12]	Wang H, Zhu X, Gao S, Chen Z 2011 Commun. Nonlinear Sci. 16 1517
[13]	Bowong S, Tewa J J 2008 Math. Comput. Model 48 1826
[14]	Chen M, Min W 2008 Phys. Lett. A 372 1595
[15]	Fradkov A L, Andrievsky B, Evans R J 2008 IEEE Circuits-I 55 1685
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施引文献

[1]	Zheng W N, Luan H X, Lü J, Yue L J 2012 J. Northeast Normal Univ. (Natural Science Edition) 44 72 (in Chinese) [郑文娜, 栾红霞, 吕晶, 岳丽娟 2012 东北师大学报(自然科学版) 44 72]
[2]	Zhu F 2008 Phys. Lett. A 372 223
[3]	Ji D H, Jeong S C, Park J H, Won S C 2012 Nonlinear Dyn. 69 1125
[4]	Zhang L W, Liao T L, Hou Y Y, Yan J J 2012 Int. J. Bifurcat. Chaos 22 1250058
[5]	Zhang Z Q, Shao H Y, Wang Z, Shen H 2012 Appl. Math. Comput. 218 7614
[6]	Guan X P, He Y H, Fan Z P 2003 Acta Phys. Sin. 52 276 (in Chinese) [关新平, 何宴辉, 范正平 2003 52 276]
[7]	Zhu F L, Xu J, Chen M Y 2012 IEEE Circuits-I 59 2702
[8]	Gao T G, Chen Z Q, Yuan Z Z, Gu Q L 2004 Acta Phys. Sin. 53 1305 (in Chinese) [高铁杠, 陈增强, 袁著祉, 顾巧论 2004 53 1305]
[9]	Chen M, Zhou D, Shang Y 2005 Chaos, Soliton. Fract. 25 573
[10]	Bowong S, Kakmeni F M M, Fotsin H 2006 Phys. Lett. A 355 193
[11]	Zhu F L 2009 Chaos, Soliton. Fract. 40 2384
[12]	Wang H, Zhu X, Gao S, Chen Z 2011 Commun. Nonlinear Sci. 16 1517
[13]	Bowong S, Tewa J J 2008 Math. Comput. Model 48 1826
[14]	Chen M, Min W 2008 Phys. Lett. A 372 1595
[15]	Fradkov A L, Andrievsky B, Evans R J 2008 IEEE Circuits-I 55 1685
[16]	Brogliato B, Heemels W P M H 2009 IEEE Trans. Automat. Control 54 1996
[17]	Fu S H, Pei L J 2010 Acta Phys. Sin. 59 5985 (in Chinese) [付士慧, 裴利军 2010 59 5985]
[18]	Wang X Y, Zhu Q L, Zhang X P 2011 Acta Phys. Sin. 60 100510 (in Chinese) [王兴元, 朱全龙, 张晓鹏 2011 60 100510]
[19]	Floquet T, Edwards C, Spurgeon S K 2007 Int. J. Adapt. Control 21 638
[20]	Li Y 2010 Nonlinear Anal.-Real. 11 713
[21]	Yan Z 2005 Chaos 15 023902
[22]	Corless M, Tu J 1998 Automatica 34 757
[23]	Mahmoud N A, Khalil H K 1996 IEEE Trans. Automat. Control 41 1402
[24]	Kalsi K, Lian J, Hui S, Zak S H 2010 Automatica 46 347
[25]	Esfandiari F, Khalil H K 1992 Int. J. Control. 56 1007

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