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The synchronization between two unknown chaotic systems is achieved by designing a controller based on the sliding mode control technique and radial basis function neural network. The controller design method is independent of the system mathematical model, but only depends on the output of the system state. Moreover, it is robust to parameter uncertainties and the outside interference. Finally, synchronization between unknown Lorenz systems and between unknown Lorenz system and Chen system are achieved using the proposed method. The response time is very short and the synchronization performance is good.
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Lü J H, Zhou T S 2002 Chaos Soliton. Fract. 14 529
[3] Yin X H, Ren Y, Shan X M 2002 Chaos Solitton. Fract. 14 1077
[4] Han X, Lu J A, Wu X 2004 Chaos Soliton. Fract. 22 221
[5] Tao C H, Lu J A, Lü J H 2002 Acta Phys. Sin. 51 1497 (in Chinese) [陶朝海、陆君安、吕金虎 2002 物理学报 51 1497]
[6] Chen Z S,Sun K H,Zhang T S 2005 Acta Phys. Sin. 54 2580 (in Chinese) [陈志胜、孙克辉、张泰山 2005 物理学报 54 2580]
[7] Sarasola C, Torrealdea F J, Anjou A D 2003 Int. J. Bifurc. Chaos 13 177
[8] Chen S H,Yang Q, Wang C P 2004 Chaos Soliton. Fract. 20 751
[9] Sun J T, Zhang Y P 2003 Phys. Lett. A 36 306
[10] Liu J, Chen S H, Lu J A 2003 Acta Phys. Sin. 52 1595 (in Chinese) [刘 杰、陈士华、陆君安 2003 物理学报 52 1595]
[11] Wang X Y,Wang Y 2007 Acta Phys. Sin. 56 2498 (in Chinese) [王兴元、王 勇 2007 物理学报 56 2498]
[12] Guo H J, Liu J H 2004 Acta Phys. Sin. 53 4080 (in Chinese) [郭会军、刘君华 2004 物理学报 53 4080]
[13] Yang S K, Chen S L, Yan H T 2002 Chaos Solition. Fract. 13 767
[14] Guan X P, Tang Y G, Fan Z P, Wang Y Q 2001 Acta Phys. Sin. 50 2112 (in Chinese) [关新平、唐英干、范正平、王益群 2001 物理学报 50 2112]
[15] Hornik K, Stinchombe M, White H 1989 Neural Networks 2 359
[16] Liu J K 2005 Matlab Simulation for Sliding Mode Control (Beijing: Tsinghua University Press) pp13—226 (in Chinese) [刘金坤 2005 滑模变结构控制MATLAB仿真(北京:清华大学出版社)第13—226页]
[17] Ropaei M, Zolghadri M 2009 Nonl. Anal. Theo. Meth. Appl. 71 4430
[18] Hajian M, Markadeh G 2009 Ener. Conv. Mana. 50 2296
[19] Kong C C, Chen S H 2009 Chin. Phys. B 18 91
[20] Yu D C, Wu A G, Yang C P 2005 Chin. Phys. B 14 914
[21] Guo H J, Yin Y W, Wang H M 2008 Chin. Phys. B 17 1652
[22] Lou X Y, Cui B T 2008 Chin. Phys. B 17 4434
[23] Li L X, Peng H P, Guan B Z, Xu J M 2001 Chin. Phys. B 10 708
[24] Yue Y J, Feng R P 2001 Acta Phys. Sin. 50 440 (in Chinese) [薛月菊、冯汝鹏 2001 物理学报 50 440]
[25] Liu D, Yan X M 2009 Acta Phys. Sin. 58 3747 (in Chinese) [刘 丁、闫晓妹 2009 物理学报 58 3747]
[26] Li X C, Xu W, Xiao Y Z 2008 Acta Phys. Sin. 57 4721 (in Chinese) [李秀春、徐 伟、肖玉柱 2008 物理学报 57 4721]
[27] Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才、宋佳秋 2008 物理学报 57 4729]
[28] Yang T, Shao H H 2005 Acta Phys. Sin. 54 4584 (in Chinese) [杨 涛、邵惠鹤 2005 物理学报 54 4584]
[29] Yau H T, Yan J J 2009 Nonl. Anal.Real World Appl. 10 1480
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Lü J H, Zhou T S 2002 Chaos Soliton. Fract. 14 529
[3] Yin X H, Ren Y, Shan X M 2002 Chaos Solitton. Fract. 14 1077
[4] Han X, Lu J A, Wu X 2004 Chaos Soliton. Fract. 22 221
[5] Tao C H, Lu J A, Lü J H 2002 Acta Phys. Sin. 51 1497 (in Chinese) [陶朝海、陆君安、吕金虎 2002 物理学报 51 1497]
[6] Chen Z S,Sun K H,Zhang T S 2005 Acta Phys. Sin. 54 2580 (in Chinese) [陈志胜、孙克辉、张泰山 2005 物理学报 54 2580]
[7] Sarasola C, Torrealdea F J, Anjou A D 2003 Int. J. Bifurc. Chaos 13 177
[8] Chen S H,Yang Q, Wang C P 2004 Chaos Soliton. Fract. 20 751
[9] Sun J T, Zhang Y P 2003 Phys. Lett. A 36 306
[10] Liu J, Chen S H, Lu J A 2003 Acta Phys. Sin. 52 1595 (in Chinese) [刘 杰、陈士华、陆君安 2003 物理学报 52 1595]
[11] Wang X Y,Wang Y 2007 Acta Phys. Sin. 56 2498 (in Chinese) [王兴元、王 勇 2007 物理学报 56 2498]
[12] Guo H J, Liu J H 2004 Acta Phys. Sin. 53 4080 (in Chinese) [郭会军、刘君华 2004 物理学报 53 4080]
[13] Yang S K, Chen S L, Yan H T 2002 Chaos Solition. Fract. 13 767
[14] Guan X P, Tang Y G, Fan Z P, Wang Y Q 2001 Acta Phys. Sin. 50 2112 (in Chinese) [关新平、唐英干、范正平、王益群 2001 物理学报 50 2112]
[15] Hornik K, Stinchombe M, White H 1989 Neural Networks 2 359
[16] Liu J K 2005 Matlab Simulation for Sliding Mode Control (Beijing: Tsinghua University Press) pp13—226 (in Chinese) [刘金坤 2005 滑模变结构控制MATLAB仿真(北京:清华大学出版社)第13—226页]
[17] Ropaei M, Zolghadri M 2009 Nonl. Anal. Theo. Meth. Appl. 71 4430
[18] Hajian M, Markadeh G 2009 Ener. Conv. Mana. 50 2296
[19] Kong C C, Chen S H 2009 Chin. Phys. B 18 91
[20] Yu D C, Wu A G, Yang C P 2005 Chin. Phys. B 14 914
[21] Guo H J, Yin Y W, Wang H M 2008 Chin. Phys. B 17 1652
[22] Lou X Y, Cui B T 2008 Chin. Phys. B 17 4434
[23] Li L X, Peng H P, Guan B Z, Xu J M 2001 Chin. Phys. B 10 708
[24] Yue Y J, Feng R P 2001 Acta Phys. Sin. 50 440 (in Chinese) [薛月菊、冯汝鹏 2001 物理学报 50 440]
[25] Liu D, Yan X M 2009 Acta Phys. Sin. 58 3747 (in Chinese) [刘 丁、闫晓妹 2009 物理学报 58 3747]
[26] Li X C, Xu W, Xiao Y Z 2008 Acta Phys. Sin. 57 4721 (in Chinese) [李秀春、徐 伟、肖玉柱 2008 物理学报 57 4721]
[27] Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才、宋佳秋 2008 物理学报 57 4729]
[28] Yang T, Shao H H 2005 Acta Phys. Sin. 54 4584 (in Chinese) [杨 涛、邵惠鹤 2005 物理学报 54 4584]
[29] Yau H T, Yan J J 2009 Nonl. Anal.Real World Appl. 10 1480
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