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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.
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Keywords:
- auxiliary drive signals /
- chaos synchronization /
- reduced-order observer /
- secure communication
[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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