混沌系统的变论域模糊控制算法研究

张巍巍; 王京; 王慧; 赵云涛

doi:10.7498/aps.60.010511

摘要

混沌运动和混沌控制受到广泛关注,本文利用模糊控制实现混沌系统的控制.针对模糊控制器精度不高,模糊控制中规则数量与控制精度之间的矛盾,提出了一种基于蚁群优化算法的变论域模糊控制器.通过分析变论域模糊控制中的2类伸缩因子,指出其中1类并不能满足广义伸缩因子条件.提出利用蚁群优化算法对伸缩因子智能寻优的方法,在对蚁群算法改进的基础上,构成一种基于蚁群算法的变论域模糊控制,将设计的控制器用于Duffing混沌系统的控制.仿真结果表明,提出的控制算法在收敛速度和稳态性能上要略优于其他控制方式.

关键词:

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:

作者及机构信息

1.
北京科技大学,高效轧制国家工程研究中心,北京 100083

基金项目: 国家高技术研究发展计划(批准号:2009AA04Z163) 资助的课题.

Authors and contacts

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

参考文献

[1]	Ke X Z, Wu Z S 1998 Acta Phys. Sin. 47 1436 (in Chinese) [柯熙政、吴振森 1998 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 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 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 55 6523]
[10]	Yu H J, Zheng N 2007 Acta Phys. Sin. 56 3782 (in Chinese)[于洪洁、郑宁 2007 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 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 55 598]
[13]	Yu D C, Meng Q H 2005 Acta Phys. Sin. 54 1092 (in Chinese)[禹东川、孟庆浩 2005 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 56 6224]
[15]	Wang D F, Han P 2006 Acta Phys. Sin. 56 1644 (in Chinese)[王东风、韩璞 2006 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 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

施引文献

[1]	Ke X Z, Wu Z S 1998 Acta Phys. Sin. 47 1436 (in Chinese) [柯熙政、吴振森 1998 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 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 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 55 6523]
[10]	Yu H J, Zheng N 2007 Acta Phys. Sin. 56 3782 (in Chinese)[于洪洁、郑宁 2007 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 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 55 598]
[13]	Yu D C, Meng Q H 2005 Acta Phys. Sin. 54 1092 (in Chinese)[禹东川、孟庆浩 2005 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 56 6224]
[15]	Wang D F, Han P 2006 Acta Phys. Sin. 56 1644 (in Chinese)[王东风、韩璞 2006 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 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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