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For a chaotic system with nonlinear ity and uncertainty, it is difficult to obtain the satisfactory performance using general control methods. A least square support vector marchine (LSSVM) control method based on particle swarm optimigation(PSO), is proposed for chaos control. Optimizing two parameters of LSSVM model by PSO abilities of the fast convergence and whole optimization, thus aroiding the blindness of man-made choice, the LSSVM-PSO model can enhance the capability of forecasting. The proposed method does not need any analytic model, and it is still effective in the presence of measurement noises. Simulation results with a Logistic mapping and Henon attractor show the effectiveness and feasibility of this method.
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Keywords:
- chaotic system control /
- particle swarm optimization /
- least squares support vector machine
[1] 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]
[2] Zhou S B, Li H, Zhu Z Z 2008 Chaos, Sol. & Frac. 36 973
[3] Jiang F, Liu S Y, Zhang J K, Gao S Y 2010 Chin. J. Comput. Phys. 27 933 (in Chinese)[姜 飞、刘三阳、张建科、高卫峰 2010 计算物理 27 933]
[4] Antonio L, Arturo Z R 2007 IEEE Trans. on Circuits. and Systems. 54 2019
[5] Guo H J, Lin S F, Liu J H 2006 Phys. Lett. A 351 257
[6] Shen L Q, Wang M 2007 Phys. Lett. A 368 379
[7] Wang X Y, Wang M J 2008 Acta Phys. Sin. 57 731(in Chinese)[王兴元、王明军 2008 物理学报 57 731]
[8] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[9] Wu L G, Ling M X, Wang C H, Zhang L X 2006 J. Harbin Institute Tech. 38 499 (in Chinese) [吴立刚、凌明祥、王常虹、张立宪 2006 哈尔滨工业大学学报 38 499]
[10] Guan X P, Fan Z P, Peng H P, Wang Y Q 2001 Acta Phys. Sin. 50 1670(in Chinese)[关新平、范正平、彭海朋、王益群 2001 物理学报 50 1670]
[11] 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 物理学报 52 531]
[12] Sukens J A K 2000 Neural Network World 10 29
[13] Ye M Y 2005 Acta Phys. Sin. 54 30(in Chinese)[叶美盈 2005 物理学报 54 30]
[14] Chappelle O, Vapnik V, Bousquet O 2002 Mach. Learn. 46 131
[15] Zhang Q X, Zhang T 2009 CIESC J. 60 1651(in Chinese)[张春晓、张 涛 2009 化工学报 60 1651]
[16] Long W, Liang X M, Xiao J H, Yan G 2009 Control and Decision 24 1513(in Chinese)[龙 文、梁昔明、肖金红、阎 纲 2009控制与决策 24 1513]
[17] Shi Y, Eberhart R C 1999 Proc. IEEE Congress on Evolutionary Computation Piscataway p1945
[18] Ratnaweera A, Halgamuge S K, Watson H C 2004 IEEE Trans. on Evolutionary Computation 8 240
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[1] 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]
[2] Zhou S B, Li H, Zhu Z Z 2008 Chaos, Sol. & Frac. 36 973
[3] Jiang F, Liu S Y, Zhang J K, Gao S Y 2010 Chin. J. Comput. Phys. 27 933 (in Chinese)[姜 飞、刘三阳、张建科、高卫峰 2010 计算物理 27 933]
[4] Antonio L, Arturo Z R 2007 IEEE Trans. on Circuits. and Systems. 54 2019
[5] Guo H J, Lin S F, Liu J H 2006 Phys. Lett. A 351 257
[6] Shen L Q, Wang M 2007 Phys. Lett. A 368 379
[7] Wang X Y, Wang M J 2008 Acta Phys. Sin. 57 731(in Chinese)[王兴元、王明军 2008 物理学报 57 731]
[8] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[9] Wu L G, Ling M X, Wang C H, Zhang L X 2006 J. Harbin Institute Tech. 38 499 (in Chinese) [吴立刚、凌明祥、王常虹、张立宪 2006 哈尔滨工业大学学报 38 499]
[10] Guan X P, Fan Z P, Peng H P, Wang Y Q 2001 Acta Phys. Sin. 50 1670(in Chinese)[关新平、范正平、彭海朋、王益群 2001 物理学报 50 1670]
[11] 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 物理学报 52 531]
[12] Sukens J A K 2000 Neural Network World 10 29
[13] Ye M Y 2005 Acta Phys. Sin. 54 30(in Chinese)[叶美盈 2005 物理学报 54 30]
[14] Chappelle O, Vapnik V, Bousquet O 2002 Mach. Learn. 46 131
[15] Zhang Q X, Zhang T 2009 CIESC J. 60 1651(in Chinese)[张春晓、张 涛 2009 化工学报 60 1651]
[16] Long W, Liang X M, Xiao J H, Yan G 2009 Control and Decision 24 1513(in Chinese)[龙 文、梁昔明、肖金红、阎 纲 2009控制与决策 24 1513]
[17] Shi Y, Eberhart R C 1999 Proc. IEEE Congress on Evolutionary Computation Piscataway p1945
[18] Ratnaweera A, Halgamuge S K, Watson H C 2004 IEEE Trans. on Evolutionary Computation 8 240
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