Research on the variable universe fuzzy algorithm of chaotic systems

Zhang Wei-Wei; Wang Jing; Wang Hui; Zhao Yun-Tao

doi:10.7498/aps.60.010511

Abstract

Chaos and chaos control received extensive attention. The fuzzy controller is used to control chaotic systems in this paper. The accuracy of fuzzy controller is not high and there is contradiction between the number of control rules and accuracy. Accordingly a variable universe fuzzy controller based on ant colony optimization algorithm is proposed. By analyzing the two kinds of contraction-expansion factors, one of them was found unable to satisfy the general contraction-expansion factor condition. A method for optimizing the contraction-expansion factors intelligently via ant colony optimization algorithm is proposed. A variable universe fuzzy controller based on ant colony optimization algorithm is constituted and used to control the Duffing chaotic system. Simulation results show that the control method is superior to the others both in convergence speed and steady-state performance.

Keywords:

Authors and contacts

1.
National Engineer Research Center of Advanced Rolling, University of Science and Technology Beijing, Beijing 100083, China

References

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[22]	Li H X 1999 Science in China (Series E) 29 32(in Chinese)[李洪兴 1999 中国科学(E辑) 29 32]
[23]	Li H X 1997 Control Theory &Applications 14 868(in Chinese)[李洪兴1997 控制理论与应用 14 868]
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Cited By

[1]	Ke X Z, Wu Z S 1998 Acta Phys. Sin. 47 1436 (in Chinese) [柯熙政、吴振森 1998 物理学报 47 1436]
[2]	Wang H X, Cai G L, Miao S, Tian L X 2010 Chen. Phys. B 329 103
[3]	Wu D H, Ke X Z 2004 Chinese Journal of Quantum Electronics 21 355(in Chinese)[兀旦晖、柯熙政 2004 量子电子学报 21 355]
[4]	Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[5]	Ott E 2002 Chaos in dynamical systems (2nd ed) (Cambridge: Cambridge University Press) p61
[6]	Wang X F, Xue H J, Si S K, Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese)[王校锋、薛红军、司守奎、姚跃亭 2009 物理学报 58 3729]
[7]	Mehta N J, Henderson R M 1991 Phys. Rev. Lett. 44 4861
[8]	Zhang X M, Peng J H, Chen G R 2004 Acta Phys. Sin. 53 2864 (in Chinese)[张晓明、彭建华、陈关荣 2004 物理学报 53 2864]
[9]	Wu C L, Ma S J, Sun Z K, Fang T 2006 Acta Phys. Sin. 55 6253 (in Chinese)[吴存利、马少娟、孙中奎、方同 2006 物理学报 55 6523]
[10]	Yu H J, Zheng N 2007 Acta Phys. Sin. 56 3782 (in Chinese)[于洪洁、郑宁 2007 物理学报 56 3782]
[11]	Li G H, Zhou S P, Xu D M, Lai J W 2000 Acta Phys. Sin. 49 2123 (in Chinese)[李国辉、周世平、徐得名、赖建文 2000 物理学报 49 2123]
[12]	Li R H, Xu W, Li S, 2006 Acta Phys. Sin. 55 598 (in Chinese)[李瑞红、徐伟、李爽 2006 物理学报 55 598]
[13]	Yu D C, Meng Q H 2005 Acta Phys. Sin. 54 1092 (in Chinese)[禹东川、孟庆浩 2005 物理学报 54 1092]
[14]	Huang G Y, Jiang C S, Wang Y H 2007 Acta Phys. Sin. 56 6224 (in Chinese)[黄国勇、姜长生、王玉惠 2007 物理学报 56 6224]
[15]	Wang D F, Han P 2006 Acta Phys. Sin. 56 1644 (in Chinese)[王东风、韩璞 2006 物理学报 56 1644]
[16]	Niu P F, Zhang J, Guan X P 2007 Acta Phys. Sin. 56 3769 (in Chinese)[牛培峰、张君、关新平 2007 物理学报 56 3769]
[17]	Tan W, Wang Y N, Duan F, Li X H 2006 Chin. Phys. 15 2529
[18]	Zheng Y G 2006 Chin. Phys. 15 2549
[19]	Zhang G L, Zeng J, Ke X Z, Deng F L 2002 Fuzzy control and MATLAB application 2002 (Xi’an: Xi’an Jiaotong University Press) p113 (in Chinese)[张国良、曾静、柯熙政、邓方林 2002 模糊控制及其MATLAB应用 (西安:西安交通大学出版社) 第113页]
[20]	Li H X 1999 Science in China (Series E)29 136(in Chinese)[李洪兴 1999 中国科学(E辑) 29 136]
[21]	Li H X 1997 Control Theory & Applications 14 868 (in Chinese)[李洪兴 1997 控制理论与应用 14 868]
[22]	Li H X 1999 Science in China (Series E) 29 32(in Chinese)[李洪兴 1999 中国科学(E辑) 29 32]
[23]	Li H X 1997 Control Theory &Applications 14 868(in Chinese)[李洪兴1997 控制理论与应用 14 868]
[24]	Li H X 2002 Science in China (Series E) 32 211(in Chinese)[李洪兴 2002 中国科学(E辑) 32 211]
[25]	Dorigo M 1997 IEEE Trans. On. Evolutionary Compute 1 53
[26]	Zhao Y T 2009 Pattern Recognition and Artificial Intelligence 22 794(in Chinese)[赵云涛 2009 模式识别与人工智能 22 794]
[27]	Liu J K 2005 Advanced PID control and MATLAB simulation (Beijing: Electronics Industry Press)p215(in Chinese)[刘金琨 2005 先进PID控制MATLAB仿真 (北京:电子工业出版社) 第211页]
[28]	Qian J L 2005 Journal of System Simulation 17 2987(in Chinese)[钱俊磊 2005 系统仿真学报 17 2987]
[29]	Tanaka K 1998 IEEE Trans. On. Circuits and Systems 45 1021
[30]	Tanaka K,Wang H O 2001 Fuzzy control systems design and analysis: a linear matrix inequality approach. (New York:John Wiley&Sons)p153—194

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Vol. 60, Issue 1 - 2011-01-05

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