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For the control of uncertainty chaos systems, a compensation control method using the polynomial-basis-functions model (PBFM) based on conjugate gradient algorithm (CGA) is studied. In the proposed method, dynamic properties of a chaotic system are first fitted by PBFM, and then feedforward compensation control for the uncertainty chaos system is implemented by using good fitting PBFM. The proposed approach can quickly track any given reference signal without the need of a mathematic model of chaos system. The numerical simulation results show that the proposed control method has not only the fast response speed and high control accuracy, but also a strong inhibitory ability to parameter perturbation and the anti-interference ability for the chaos system.
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Keywords:
- chaotic control /
- polynomial-basis-functions model (PBFM) /
- conjugate gradient algorithm (CGA)
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[2] Sugawara T, Tachikawa M, Tsukamoto T, Shimizu T 1994 Phys. Rev. Lett. 72 3502
[3] Lu J A, Wu X Q, L J H 2002 Phys. Lett. A 305 365
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[10] GUAN X P, HE Y H 2004 Chin. Phys. Lett. 21 0227
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[12] Gao J F, Yao L N 2002 Acta Phys. Sin. 51 0487 (in Chinese) [高金峰, 姚利娜 2002 物理学报 51 0487]
[13] Ma X K, Zhang J 2003 Acta Phys. Sin. 52 2415 (in Chinese) [马西奎, 张浩 2003 物理学报 52 2415]
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[18] Pyragas K 1992 Phys. Lett. A 170 421
[19] Pyragas K 1993 Phys. Lett. A 180 99
[20] Tang G N, Luo X S, Kong L J 2000 Acta Phys. Sin. 49 0030 (in Chinese) [唐国宁, 罗晓曙, 孔令江 2000 物理学报 49 0030]
[21] 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 物理学报 50 2108]
[22] 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]
[23] Gao X, Liu X W 2007 Acta Phys. Sin. 56 0084 (in Chinese) [高心, 刘兴文 2007 物理学报 56 0084]
[24] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese) [王发强, 刘崇新 2006 物理学报 55 5055]
[25] Chen X P, Hao J B 2009 Acta Phys. Sin. 58 2914 (in Chinese) [陈光平, 郝加波 2009 物理学报 58 2914]
[26] 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 物理学报 58 3729]
[27] Luo X H, Li H Q, Chen QH 2009 Acta Phys. Sin. 58 7532 (in Chinese) [罗小华, 李华青, 陈秋华 2009 物理学报 58 7532]
[28] 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 物理学报 60 019501]
[29] 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 物理学报 50 629]
[30] Wang X Y, Shi Q J 2005 Acta Phys. Sin. 54 5591 (in Chinese) [王兴元, 石其江 2005 物理学报 54 5591]
[31] Ning D,Lu J A 2005 Acta Phys. Sin. 54 4590 (in Chinese) [宁娣, 陆君安 2005 物理学报 54 4590]
[32] Wu W G, Gu T X 2000 Acta Phys. Sin. 49 1922 (in Chinese) [伍维根, 古天祥 2000 物理学报 49 1922]
[33] Lig 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 物理学报 52 181]
[34] Liu D, Ren H P, Kong Z Q 2003 Acta Phys. Sin. 52 0531 (in Chinese) [刘丁, 任海鹏, 孔志强 2003 物理学报 52 0531]
[35] Zeng Z Z 2013 Acta Phys. Sin. 62 030504 (in Chinese) [曾喆昭 2013 物理学报 62 030504]
[36] Lin D, Wang X Y 2010 Fuzzy Sets and Systems 161 2066
[37] Lin D, Wang X Y 2011 Neurocomputing 74 2241
[38] Wang T S, Wang X Y, Wang M J 2011 Communications in Nonlinear Science and Numerical Simulation 16 3367
[39] Zeng Z Z 2012 Neural Calculation Principle and its Application Technology (Beijing: Science Press) p26 (in Chinese) [曾喆昭 2012 神经计算原理及其应用技术(北京: 科学出版社) 第26页]
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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, L 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 物理学报 59 2250]
[5] Liu J, Chen S H, Lu J A etc. 2002 Chin. Phys. 11 233
[6] Li Z, Han C Z 2002 Chin. Phys. 11 0009
[7] Li Z, Han C Z 2001 Chin. Phys. 10 0494
[8] Li L X, Peng H P, Xu J M etc. 2001 Chin. Phys. 10 0708
[9] Sun F Y 2006 Chin. Phys. Lett. 23 0032
[10] GUAN X P, HE Y H 2004 Chin. Phys. Lett. 21 0227
[11] Tan W, Wang Y N, Liu Z R 2002 Acta Phys. Sin. 51 2463 (in Chinese) [谭文, 王耀南, 刘祖润 2002 物理学报 51 2463]
[12] Gao J F, Yao L N 2002 Acta Phys. Sin. 51 0487 (in Chinese) [高金峰, 姚利娜 2002 物理学报 51 0487]
[13] Ma X K, Zhang J 2003 Acta Phys. Sin. 52 2415 (in Chinese) [马西奎, 张浩 2003 物理学报 52 2415]
[14] Cao Z D, He G G 2001 Acta Phys. Sin. 50 2103 (in Chinese) [曹志彤, 何国光 2001 物理学报 50 2103]
[15] Han C Z, Li Z 2001 Acta Phys. Sin. 50 2103 (in Chinese) [韩崇昭, 李智 2001 物理学报 50 0847]
[16] Tang G N, Hu G 2006 Chin. Phys. Lett. 23 1523
[17] Ott E, Grebogi C, Yorke A J 1990 Phys. Rev. Lett. 64 1196
[18] Pyragas K 1992 Phys. Lett. A 170 421
[19] Pyragas K 1993 Phys. Lett. A 180 99
[20] Tang G N, Luo X S, Kong L J 2000 Acta Phys. Sin. 49 0030 (in Chinese) [唐国宁, 罗晓曙, 孔令江 2000 物理学报 49 0030]
[21] 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 物理学报 50 2108]
[22] 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]
[23] Gao X, Liu X W 2007 Acta Phys. Sin. 56 0084 (in Chinese) [高心, 刘兴文 2007 物理学报 56 0084]
[24] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese) [王发强, 刘崇新 2006 物理学报 55 5055]
[25] Chen X P, Hao J B 2009 Acta Phys. Sin. 58 2914 (in Chinese) [陈光平, 郝加波 2009 物理学报 58 2914]
[26] 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 物理学报 58 3729]
[27] Luo X H, Li H Q, Chen QH 2009 Acta Phys. Sin. 58 7532 (in Chinese) [罗小华, 李华青, 陈秋华 2009 物理学报 58 7532]
[28] 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 物理学报 60 019501]
[29] 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 物理学报 50 629]
[30] Wang X Y, Shi Q J 2005 Acta Phys. Sin. 54 5591 (in Chinese) [王兴元, 石其江 2005 物理学报 54 5591]
[31] Ning D,Lu J A 2005 Acta Phys. Sin. 54 4590 (in Chinese) [宁娣, 陆君安 2005 物理学报 54 4590]
[32] Wu W G, Gu T X 2000 Acta Phys. Sin. 49 1922 (in Chinese) [伍维根, 古天祥 2000 物理学报 49 1922]
[33] Lig 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 物理学报 52 181]
[34] Liu D, Ren H P, Kong Z Q 2003 Acta Phys. Sin. 52 0531 (in Chinese) [刘丁, 任海鹏, 孔志强 2003 物理学报 52 0531]
[35] Zeng Z Z 2013 Acta Phys. Sin. 62 030504 (in Chinese) [曾喆昭 2013 物理学报 62 030504]
[36] Lin D, Wang X Y 2010 Fuzzy Sets and Systems 161 2066
[37] Lin D, Wang X Y 2011 Neurocomputing 74 2241
[38] Wang T S, Wang X Y, Wang M J 2011 Communications in Nonlinear Science and Numerical Simulation 16 3367
[39] Zeng Z Z 2012 Neural Calculation Principle and its Application Technology (Beijing: Science Press) p26 (in Chinese) [曾喆昭 2012 神经计算原理及其应用技术(北京: 科学出版社) 第26页]
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