基于神经网络的混沌控制研究
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摘要
混沌被誉为非线性系统中的一朵奇葩，混沌控制在实际应用中显示出广阔的前景。人们对混沌控制展开了深入研究，提出了多种控制方法。但是，由于混沌系统动力学行为的复杂性和独特性，迄今，混沌系统的控制理论还很不成熟，特别是对系统数学模型难以准确建立、先知条件较少的情况下，传统的控制方法难以奏效。自20世纪80年代以来，神经网络研究取得很大进展，许多网络模型已被广泛地应用于模式识别、图像处理、语言处理等领域，神经网络能够学习任意连续非线性函数，决定了它们在处理高度非线性和严重不确定系统的控制方面存在巨大的潜力。
本文研究了电子和电路系统存在的混沌现象的神经网络控制问题，其中包括两个方面的内容：混沌系统的神经网络辨识技术和基于神经网络的混沌控制。
首先，在分析了在系统辨识过程中应用比较多的基本BP算法及其改进算法的优缺点的基础上，将附加动量项和自适应变学习率两种算法的优点相结合，给出了一种新的改进的BP算法，并将其用于BP神经网络的Lorenz混沌系统辨识研究，仿真结果表明所提出的算法的辨识效果优于单独附加动量项或自适应变学习率的BP算法。
其次，给出了神经网络应用于混沌系统控制的几种结构，并采用了模型参考自适应控制结构，利用B-样条神经网络对Henon混沌系统进行了控制仿真研究，其结果表明，该方法比BP神经网络控制混沌更有效。
最后，为了对未知多变量的混沌系统进行有效的控制，采用了动态神经网络控制未知多变量Lorenz混沌系统，利用计算机仿真证明了将动态神经网络引入混沌控制的可行性。
The control of chaotic systems has capacious application foreground, a great number of method for the control of chaotic systems has been brought out. However, control theory of chaotic systems is still not perfect so far because of the complexity and particularity of the dynamic behavior in chaotic systems. Especially when the mathematic model of the system cannot be actually constructed and little preconditions be attained, classic control methods not act that well. Since 1980's, the research of neural networks has made great progresses, which has already proved that the neural networks ean approach any continuous nonlinear function. Characteristics of neural networks make it has considerable potential when be used to control a system which is highly nonlinear or uncertain.
In this paper, research concentrates on the neural network control of chaotic systems in electronics and circuits systems, including two fields: chaotic systems identification and chaotic control.
Firstly, based on the analysis of advantages and disadvantages of basic back-propagation neural network and ameliorating arithmetic in the process of systems' identification, a new ameliorating arithmetic which is the combination of additional momentum and adaptive momentum method has been presented, and then identifying Lorenz chaotic system is carefully studied by using of the new method. Results of the numerical simulation demonstrate that the newly presented scheme is of great effectiveness.
Secondly, several kind of neural network controlling structures which apply to chaotic systems are given out, adopted reference model and self-adaptive controlling structure are consulted. This paper put
much energy into the simulation of B-spline neural network in Lorenz chaotic system. Results of computer simulation clearly show that this method is much more effective as compared whit back-propagation neural networks.
At last, in order to control unknown multivariable chaotic systems effectively, dynamical neural network is employed to control the unknown multivariable Lorenz chaotic system. Computer simulation elementary demonstrated the application feasibility of dynamical neural network in chaotic control.
本文研究了电子和电路系统存在的混沌现象的神经网络控制问题，其中包括两个方面的内容：混沌系统的神经网络辨识技术和基于神经网络的混沌控制。
首先，在分析了在系统辨识过程中应用比较多的基本BP算法及其改进算法的优缺点的基础上，将附加动量项和自适应变学习率两种算法的优点相结合，给出了一种新的改进的BP算法，并将其用于BP神经网络的Lorenz混沌系统辨识研究，仿真结果表明所提出的算法的辨识效果优于单独附加动量项或自适应变学习率的BP算法。
其次，给出了神经网络应用于混沌系统控制的几种结构，并采用了模型参考自适应控制结构，利用B-样条神经网络对Henon混沌系统进行了控制仿真研究，其结果表明，该方法比BP神经网络控制混沌更有效。
最后，为了对未知多变量的混沌系统进行有效的控制，采用了动态神经网络控制未知多变量Lorenz混沌系统，利用计算机仿真证明了将动态神经网络引入混沌控制的可行性。
The control of chaotic systems has capacious application foreground, a great number of method for the control of chaotic systems has been brought out. However, control theory of chaotic systems is still not perfect so far because of the complexity and particularity of the dynamic behavior in chaotic systems. Especially when the mathematic model of the system cannot be actually constructed and little preconditions be attained, classic control methods not act that well. Since 1980's, the research of neural networks has made great progresses, which has already proved that the neural networks ean approach any continuous nonlinear function. Characteristics of neural networks make it has considerable potential when be used to control a system which is highly nonlinear or uncertain.
In this paper, research concentrates on the neural network control of chaotic systems in electronics and circuits systems, including two fields: chaotic systems identification and chaotic control.
Firstly, based on the analysis of advantages and disadvantages of basic back-propagation neural network and ameliorating arithmetic in the process of systems' identification, a new ameliorating arithmetic which is the combination of additional momentum and adaptive momentum method has been presented, and then identifying Lorenz chaotic system is carefully studied by using of the new method. Results of the numerical simulation demonstrate that the newly presented scheme is of great effectiveness.
Secondly, several kind of neural network controlling structures which apply to chaotic systems are given out, adopted reference model and self-adaptive controlling structure are consulted. This paper put
much energy into the simulation of B-spline neural network in Lorenz chaotic system. Results of computer simulation clearly show that this method is much more effective as compared whit back-propagation neural networks.
At last, in order to control unknown multivariable chaotic systems effectively, dynamical neural network is employed to control the unknown multivariable Lorenz chaotic system. Computer simulation elementary demonstrated the application feasibility of dynamical neural network in chaotic control.
引文
[1] H．舒斯特著，朱雄、林圭年译，混沌学引论，上海科技教育出版社，1993年9月
[2] 龙运佳，混沌震动研究方法与实际，清华大学出版社，1997年4月
[3] 王东生，曹磊，混沌、分形及其应用，中国科技大学出版社，1995
[4] F.Takens, Setecting strange attractors in fluid turbulence,in:Dynamical systems and Turbulence,eds.D.Rand and L.A.Young(Springer,Berlin,1981
[5] 陈士华，陆均安，混沌动力学初步，武汉电力大学出版社，1998年8月
[6] 张家树，混沌信号的非线性自适应预测技术及其应用研究，电子科技大学博士论文，2001年1月
[7] 郑为敏，正反馈，清华大学出版社，1998年3月-12
[8] Alsing PM,Garielides A Using neural networks for controlling chaos Phys Rev E, 1994, 49: 1225-1231
[9] OtawaraK,Fan LT Controlling chaos with an artificial neural networks in Proc IEEE Int Joint ConfFuzzy Syst,1995,4:1943-1948
[10] Lin CT Controlling chaos by GA based reinforcement learning neural network IEEE Transactions on Neural Networks, 1999,10:846-859
[11] Huberman BA Dynamics of adaptive systems IEEE Transon Circuits and Systems, 1990,37(4):547-550
[12] Sinha S Adaptive control in nonlinear dynamics Phys D,1990,43:118-125
[13] Vassiliadis D Parametric adative control and parameter identification of lowdimentional chaotic systems Phys D,1994,71:319-341
[14] Chen Liang,Chen Guanrong.Fuzzy predictive control funcerta in chaotic systems using time series International Joural of Bifurcation and Chaos,1999,9(4):757-767
[15] Oscar Fuzzy control of chaos International Journal of Bifurcation and Chaos,1998,8(8):1743-1747
[16] 梁志珊 应用混沌理论的电力系统短期负荷预测控制与决策，1998，13(1)：87-90
[17] Packard NN Geometry from a times series Phys Rev Lett,1980,45:712-717
[18] Takens F Dynamical systems and turbulence Springer Verlag,1981,10:366-381
[19] KumartA Attactors imecsion, entropy and modeling of speech time series Electron Lett 1990, 26(21):1790-1792
[20] 童勤业 混沌理论在测量中的应用 电子科学学刊，1999，21(1)，42-49
[21] 王宁 基于嵌入混沌序列的遗传算法 系统工程理论与实践，1999，6：1-7
[22] Tse CK Flipbifurcation and chaos in three state boost switching regulators IEEE Trans Circuits Systems 2,1994,41(1):16-23
[23] C.K.Tse,Flip bifurcation and chaos in three-state boost switching regulators,IEEE Trans.Circults Syst.Ⅱ, vol.41 no.1,pp.19-23,1994.
[24] L.Chen,Global searching ability of chaotic neural networks,IEEE Trans.Circults Syst.Ⅱ,vol.46,no.8,pp.626-632,1999.
[25] In V, "Experimental maintenance of chaos." Physcial R,L.,74:4420-4423, 1995.
[26] Poon L, "Controlling complexity", Phusical Review Letters,75:4023-4026, 1995.
[27] Mehta NJ, "Controlling chaos to generate a periodic orbits", P.R.A.,44: 4861-4865,1991.
[28] Carroll T L, "Trackong unstable orbits in an experiment." P.R.A.,46: 6189-6192,1992.
[29] Marwell,J.C.,OnGovermors,Proceedingsof the Royal Society of London, Vol. 16,270-283, 1868
[30] 王宁，涂健，陈锦江，是用单个自适应神经元的智能控制，《华中理工
大学学报》，21(3)：31-35，1993．
[31] 徐永群等．BP神经网络计算法及其应用研究《黄冈师范学院学报》，2000年6月(3)
[32] 李新忠，简林柯，何钺．基于神经网络的优化控制．机械工业自动化．Vol．19．No．2，24-26，1997
[33] 阮晓钢．非线性逆神经元解耦飞行控制方法．航空学报，Vol．18，No．1，1997
[34] 胡泽新．神经网络自适应控制系统研究．控制与决策．Vol．7，No．5．361-366，1995
[35] Hoskins,J.N.Hwang and J.Vagners,Iterative Inversion of Neural Networks and Its Application to Adaptive Control, IEEE Trans. on Neural Networks, Vol.3,No.2,292-301,1992
[36] 胡守仁主编．神经网络应用技术．国防科技大学出版社，1993
[37] 戴琼海、柴天佑等．一类未知多变量非线性系统的动态神经网络自适应控制 信息与控制Vol．25，No．6 1996：332-338
[38] 李冬梅，王正欧 等．混沌系统的神经网络预测控制．控制与决策．Vol．17，No．6 2002
[39] 李士勇．模糊控制、神经网络控制和智能控制．哈尔滨工业大学出版社，1996
[40] 郝柏林．从抛物线谈起———混沌动力学引论[M]．上海：上海科技教育出版社，1993
[41] 汤同奎，邵惠鹤．神经网络在控制中的应用[J]．江苏石油化．工学院学报，1998，10(1)：45—49
[42] 宋浩，蔡遵生，赵学庄，等．一种控制化学混沌的新方法———在全混沌区的非线性人工神经网络偶然微扰反馈控制[J]．中国科学(B辑)，2000，30(1)：8—14
[43] 神经网络在混沌系统控制中的应用研究进展
[44] 刘廷章 回转类复杂曲面加工精度的自适应与智能控制策略研究，西安
交通大学博士学位论文，1996
[45] 王东生，混沌、分形及其应用，中国科技大学出版社
[46] 李裴然，利用时间序列重构用此同步电动机混沌吸引子，控制与决策，2001．3
[47] Sanchez EdgarN, Perez JoseP, Ricalde LuisJ etal Chaos synchronization via adaptive recurrent neural control[J].Proceedings of the IEEE Conference on Decision and Control,2001,(4):3536-3539
[48] Zhong GQ, Bargar R, Halle K S.Circuits for Voltage Tuning the Parameters of Chua's Circuit:Experimental Application for Musical Signal Generation[J].J.of the Franklin Institute,1994,331(6):743-784
[49] Kapitaniak T, Chua LO, Zhong GO. Experimental Synchronization of Chaos Using Continuous Control[J].Int.J.Bifurcation Choas,19944(2):483-488
[50] Chua L O,Yang T. Adaptive Synchronization of Chua's Oscillators[J].Int. J. B furcation Choas,1996,6(1):189-201
[51] Suykens J A K, Curran P F. Robust Nonlinear Synchronization of Chaotic Lure Systems[J].IEEETrans.Circuit Syst.,1997,44(10):891-904
[52] 关新平，范正平，陈彩莲，华长春．混沌控制及其在保密通信中应用．北京国防工业出版社，2002，22-34
[53] 於东军．B样条神经网络的构造理论．计算机研究与发展，1999，5
[54] 孙增圻等编著．智能控制与技术．北京：清华大学出版社，1997，158-168
[55] 靳蕃．神经网络计算智能基础原理．方法．成都：西南交通大学出版社，2000．
[2] 龙运佳，混沌震动研究方法与实际，清华大学出版社，1997年4月
[3] 王东生，曹磊，混沌、分形及其应用，中国科技大学出版社，1995
[4] F.Takens, Setecting strange attractors in fluid turbulence,in:Dynamical systems and Turbulence,eds.D.Rand and L.A.Young(Springer,Berlin,1981
[5] 陈士华，陆均安，混沌动力学初步，武汉电力大学出版社，1998年8月
[6] 张家树，混沌信号的非线性自适应预测技术及其应用研究，电子科技大学博士论文，2001年1月
[7] 郑为敏，正反馈，清华大学出版社，1998年3月-12
[8] Alsing PM,Garielides A Using neural networks for controlling chaos Phys Rev E, 1994, 49: 1225-1231
[9] OtawaraK,Fan LT Controlling chaos with an artificial neural networks in Proc IEEE Int Joint ConfFuzzy Syst,1995,4:1943-1948
[10] Lin CT Controlling chaos by GA based reinforcement learning neural network IEEE Transactions on Neural Networks, 1999,10:846-859
[11] Huberman BA Dynamics of adaptive systems IEEE Transon Circuits and Systems, 1990,37(4):547-550
[12] Sinha S Adaptive control in nonlinear dynamics Phys D,1990,43:118-125
[13] Vassiliadis D Parametric adative control and parameter identification of lowdimentional chaotic systems Phys D,1994,71:319-341
[14] Chen Liang,Chen Guanrong.Fuzzy predictive control funcerta in chaotic systems using time series International Joural of Bifurcation and Chaos,1999,9(4):757-767
[15] Oscar Fuzzy control of chaos International Journal of Bifurcation and Chaos,1998,8(8):1743-1747
[16] 梁志珊 应用混沌理论的电力系统短期负荷预测控制与决策，1998，13(1)：87-90
[17] Packard NN Geometry from a times series Phys Rev Lett,1980,45:712-717
[18] Takens F Dynamical systems and turbulence Springer Verlag,1981,10:366-381
[19] KumartA Attactors imecsion, entropy and modeling of speech time series Electron Lett 1990, 26(21):1790-1792
[20] 童勤业 混沌理论在测量中的应用 电子科学学刊，1999，21(1)，42-49
[21] 王宁 基于嵌入混沌序列的遗传算法 系统工程理论与实践，1999，6：1-7
[22] Tse CK Flipbifurcation and chaos in three state boost switching regulators IEEE Trans Circuits Systems 2,1994,41(1):16-23
[23] C.K.Tse,Flip bifurcation and chaos in three-state boost switching regulators,IEEE Trans.Circults Syst.Ⅱ, vol.41 no.1,pp.19-23,1994.
[24] L.Chen,Global searching ability of chaotic neural networks,IEEE Trans.Circults Syst.Ⅱ,vol.46,no.8,pp.626-632,1999.
[25] In V, "Experimental maintenance of chaos." Physcial R,L.,74:4420-4423, 1995.
[26] Poon L, "Controlling complexity", Phusical Review Letters,75:4023-4026, 1995.
[27] Mehta NJ, "Controlling chaos to generate a periodic orbits", P.R.A.,44: 4861-4865,1991.
[28] Carroll T L, "Trackong unstable orbits in an experiment." P.R.A.,46: 6189-6192,1992.
[29] Marwell,J.C.,OnGovermors,Proceedingsof the Royal Society of London, Vol. 16,270-283, 1868
[30] 王宁，涂健，陈锦江，是用单个自适应神经元的智能控制，《华中理工
大学学报》，21(3)：31-35，1993．
[31] 徐永群等．BP神经网络计算法及其应用研究《黄冈师范学院学报》，2000年6月(3)
[32] 李新忠，简林柯，何钺．基于神经网络的优化控制．机械工业自动化．Vol．19．No．2，24-26，1997
[33] 阮晓钢．非线性逆神经元解耦飞行控制方法．航空学报，Vol．18，No．1，1997
[34] 胡泽新．神经网络自适应控制系统研究．控制与决策．Vol．7，No．5．361-366，1995
[35] Hoskins,J.N.Hwang and J.Vagners,Iterative Inversion of Neural Networks and Its Application to Adaptive Control, IEEE Trans. on Neural Networks, Vol.3,No.2,292-301,1992
[36] 胡守仁主编．神经网络应用技术．国防科技大学出版社，1993
[37] 戴琼海、柴天佑等．一类未知多变量非线性系统的动态神经网络自适应控制 信息与控制Vol．25，No．6 1996：332-338
[38] 李冬梅，王正欧 等．混沌系统的神经网络预测控制．控制与决策．Vol．17，No．6 2002
[39] 李士勇．模糊控制、神经网络控制和智能控制．哈尔滨工业大学出版社，1996
[40] 郝柏林．从抛物线谈起———混沌动力学引论[M]．上海：上海科技教育出版社，1993
[41] 汤同奎，邵惠鹤．神经网络在控制中的应用[J]．江苏石油化．工学院学报，1998，10(1)：45—49
[42] 宋浩，蔡遵生，赵学庄，等．一种控制化学混沌的新方法———在全混沌区的非线性人工神经网络偶然微扰反馈控制[J]．中国科学(B辑)，2000，30(1)：8—14
[43] 神经网络在混沌系统控制中的应用研究进展
[44] 刘廷章 回转类复杂曲面加工精度的自适应与智能控制策略研究，西安
交通大学博士学位论文，1996
[45] 王东生，混沌、分形及其应用，中国科技大学出版社
[46] 李裴然，利用时间序列重构用此同步电动机混沌吸引子，控制与决策，2001．3
[47] Sanchez EdgarN, Perez JoseP, Ricalde LuisJ etal Chaos synchronization via adaptive recurrent neural control[J].Proceedings of the IEEE Conference on Decision and Control,2001,(4):3536-3539
[48] Zhong GQ, Bargar R, Halle K S.Circuits for Voltage Tuning the Parameters of Chua's Circuit:Experimental Application for Musical Signal Generation[J].J.of the Franklin Institute,1994,331(6):743-784
[49] Kapitaniak T, Chua LO, Zhong GO. Experimental Synchronization of Chaos Using Continuous Control[J].Int.J.Bifurcation Choas,19944(2):483-488
[50] Chua L O,Yang T. Adaptive Synchronization of Chua's Oscillators[J].Int. J. B furcation Choas,1996,6(1):189-201
[51] Suykens J A K, Curran P F. Robust Nonlinear Synchronization of Chaotic Lure Systems[J].IEEETrans.Circuit Syst.,1997,44(10):891-904
[52] 关新平，范正平，陈彩莲，华长春．混沌控制及其在保密通信中应用．北京国防工业出版社，2002，22-34
[53] 於东军．B样条神经网络的构造理论．计算机研究与发展，1999，5
[54] 孙增圻等编著．智能控制与技术．北京：清华大学出版社，1997，158-168
[55] 靳蕃．神经网络计算智能基础原理．方法．成都：西南交通大学出版社，2000．