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For the problem of controlling uncertain chaotic systems, a method of feedback compensation control based on the radial basis function neural network (RBFNN) is studied. In the proposed method, dynamic properties of chaotic system is first trained by RBFNN, and then feedback compensation control for chaotic system is implemented using trained good RBFNN model. The characteristics of this method is that this method can quickly track any given reference signal with on requirement for any mathematic model of controlled chaos system. The numerical simulation results show that the proposed control method not only has the fast response speed, high control accuracy, but also has a stronger ability to suppress parameter perturbation and to resist interference to chaos system.
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Keywords:
- chaotic control /
- RBF neural network /
- feedback control /
- error compensation
[1] Colet P, Roy R 1994 Opt. Lett. 19 2056
[2] Sugawara T, Tachikawa M, Tsukamoto T, Shimizu T 1994 Phys. Rev. Lett. 72 3502
[3] Lu J A, Wu X Q, Lü J H 2002 Phys. Lett. A 305 365
[4] Zhu S P, Qian F C, Liu D 2010 Acta Phys. Sin. 59 2250 (in Chinese) [朱少平, 钱富才, 刘丁 2010 59 2250]
[5] Ott E, Grebogi C, Yorke A J 1990 Phys. Rev. Lett. 64 1196
[6] Pyragas K 1992 Phys. Lett. A 170 421
[7] Pyragas K 1993 Phys. Lett. A 180 99
[8] Tang G N, Luo X S, Kong L J 2000 Acta Phys. Sin. 49 30 (in Chinese) [唐国宁, 罗晓曙, 孔令江 2000 49 30]
[9] Guan X P, Fan Z P, Peng H P, Wang Y Q 2001 Acta Phys. Sin. 50 2108 (in Chinese) [关新平, 范正平, 彭海朋, 王益群 2001 50 2108]
[10] Song Y Z, Zhao G Z, Qi D L 2007 Control Theory and Applications 24 795 (in Chinese) [宋运忠, 赵光宙, 齐冬莲 2007 控制理论与应用 24 795]
[11] Gao X, Liu X W 2007 Acta Phys. Sin. 56 84 (in Chinese) [高心, 刘兴文 2007 56 84]
[12] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 ( in Chinese) [王发强, 刘崇新 2006 55 5055]
[13] Chen G P, Hao J B 2009 Acta Phys. Sin. 58 2914 (in Chinese) [陈光平, 郝加波 2009 58 2914]
[14] Wang X F, Xue H J, Si S K, Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) [王晓锋, 薛红军, 司守奎, 姚跃亭 2009 58 3729]
[15] Luo X H, Li H Q, Chen Q H 2009 Acta Phys. Sin. 58 7532 (in Chinese) [罗小华, 李华青, 陈秋华 2009 58 7532]
[16] Liu Z H, Zhang Y J, Zhang J, Wu J H 2011 Acta Phys. Sin. 60 019501 (in Chinese) [刘朝华, 张英杰, 章兢, 吴建辉 2011 60 019501
[17] Li L X, Peng H P, Lu H B 2001 Acta Phys. Sin. 50 629 (in Chinese) [李丽香, 彭海朋, 卢辉斌 2001 50 629]
[18] Wang X Y, Shi Q J 2005 Acta Phys. Sin. 54 5591 (in Chinese) [王兴元, 石其江 2005 54 5591]
[19] Ning D, Lu J A 2005 Acta Phys. Sin. 54 4590 (in Chinese) [宁娣, 陆君安 2005 54 4590]
[20] Wu W G, Gu T X 2000 Acta Phys. Sin. 49 1922 (in Chinese) [伍维根, 古天祥2000 49 1922]
[21] Li G H, Xu D M, Zhou S P 2003 Acta Phys. Sin. 52 181 (in Chinese) [李国辉, 徐得名, 周世平 2003 52 181]
[22] Liu D, Ren H P, Kong Z Q 2003 Acta Phys. Sin. 52 531 (in Chinese) [刘丁, 任海鹏, 孔志强 2003 52 531]
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[1] Colet P, Roy R 1994 Opt. Lett. 19 2056
[2] Sugawara T, Tachikawa M, Tsukamoto T, Shimizu T 1994 Phys. Rev. Lett. 72 3502
[3] Lu J A, Wu X Q, Lü J H 2002 Phys. Lett. A 305 365
[4] Zhu S P, Qian F C, Liu D 2010 Acta Phys. Sin. 59 2250 (in Chinese) [朱少平, 钱富才, 刘丁 2010 59 2250]
[5] Ott E, Grebogi C, Yorke A J 1990 Phys. Rev. Lett. 64 1196
[6] Pyragas K 1992 Phys. Lett. A 170 421
[7] Pyragas K 1993 Phys. Lett. A 180 99
[8] Tang G N, Luo X S, Kong L J 2000 Acta Phys. Sin. 49 30 (in Chinese) [唐国宁, 罗晓曙, 孔令江 2000 49 30]
[9] Guan X P, Fan Z P, Peng H P, Wang Y Q 2001 Acta Phys. Sin. 50 2108 (in Chinese) [关新平, 范正平, 彭海朋, 王益群 2001 50 2108]
[10] Song Y Z, Zhao G Z, Qi D L 2007 Control Theory and Applications 24 795 (in Chinese) [宋运忠, 赵光宙, 齐冬莲 2007 控制理论与应用 24 795]
[11] Gao X, Liu X W 2007 Acta Phys. Sin. 56 84 (in Chinese) [高心, 刘兴文 2007 56 84]
[12] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 ( in Chinese) [王发强, 刘崇新 2006 55 5055]
[13] Chen G P, Hao J B 2009 Acta Phys. Sin. 58 2914 (in Chinese) [陈光平, 郝加波 2009 58 2914]
[14] Wang X F, Xue H J, Si S K, Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) [王晓锋, 薛红军, 司守奎, 姚跃亭 2009 58 3729]
[15] Luo X H, Li H Q, Chen Q H 2009 Acta Phys. Sin. 58 7532 (in Chinese) [罗小华, 李华青, 陈秋华 2009 58 7532]
[16] Liu Z H, Zhang Y J, Zhang J, Wu J H 2011 Acta Phys. Sin. 60 019501 (in Chinese) [刘朝华, 张英杰, 章兢, 吴建辉 2011 60 019501
[17] Li L X, Peng H P, Lu H B 2001 Acta Phys. Sin. 50 629 (in Chinese) [李丽香, 彭海朋, 卢辉斌 2001 50 629]
[18] Wang X Y, Shi Q J 2005 Acta Phys. Sin. 54 5591 (in Chinese) [王兴元, 石其江 2005 54 5591]
[19] Ning D, Lu J A 2005 Acta Phys. Sin. 54 4590 (in Chinese) [宁娣, 陆君安 2005 54 4590]
[20] Wu W G, Gu T X 2000 Acta Phys. Sin. 49 1922 (in Chinese) [伍维根, 古天祥2000 49 1922]
[21] Li G H, Xu D M, Zhou S P 2003 Acta Phys. Sin. 52 181 (in Chinese) [李国辉, 徐得名, 周世平 2003 52 181]
[22] Liu D, Ren H P, Kong Z Q 2003 Acta Phys. Sin. 52 531 (in Chinese) [刘丁, 任海鹏, 孔志强 2003 52 531]
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