基于粒子群算法自适应逆控制混沌同步研究
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摘要
由于混沌具有对初始条件极端敏感、似噪声、连续宽频谱等特性,近年来在保密通信等领域得到了深入的研究和广泛的应用。但是,目前混沌控制和混沌同步理论并不成熟,还有很多理论和技术上的问题需要解决。针对目前混沌同步研究中存在的一些问题,本文以连续和离散混沌系统为研究对象,通过对混沌同步理论、混沌同步方法及其应用等相关问题的研究,为混沌同步及其应用提供理论方法和扩充理论基础。
首先,针对粒子群优化算法(PSO)易陷入早熟陷阱的缺点,本文提出改进型粒子群优化算法(MPSO)和蜜蜂进化型粒子群优化算法(BEMPSO)。本文对五个典型的测试函数分别用不同的粒子群优化算法进行了优化仿真实验,并对实验结果进行了比较和分析,得出BEMPSO具有很好的收敛性。这些理论的研究将为本文以后章节的研究提供有力的研究依据。
其次,为了实现连续和离散混沌系统建模,将分层递阶蜜蜂进化型粒子群优化(DDBEMPSO)算法用于神经网络训练,给出了基于DDBEMPSO的RBF神经网络学习算法的设计方法和基于DDBEMPSO的混沌神经网络学习算法的设计方法。通过连续和离散混沌映射时间序列预测的仿真实验,得出分层递阶蜜蜂进化型粒子群优化方法提高了搜索效率,克服了早熟现象,提高了收敛性,取得了较好的仿真结果。
再次,针对混沌信号受到信道噪声的影响,难以很好的达到同步问题,基于自适应逆的原理设计了自适应逆控制器,引入到混沌同步,对系统中存在的扰动和噪声进行了消除,取得了很好的效果。自适应逆控制对于消除信号中的噪声具有最优性,非常适合在混沌同步中应用。并采用此方法对噪声干扰的离散混沌系统和连续混沌系统同步仿真研究,对比利用DDBEMPSO优化RBFNN和CNN用于辨识和控制离散混沌系统同步数字仿真,可知对离散混沌系统来说,采用CNN结构构造辨识器和控制器比采用RBFNN结构构造辨识器和控制器性能更优越。
最后,详细地介绍了基于混沌同步的振幅隐蔽调制保密通信原理,并对自适应逆控制的振幅隐蔽调制离散混沌同步步骤加以说明。分别以Logistic映设和Lorenz连续混沌系统为例进行仿真研究。重点阐述了超混沌同步的保密通信,分析四维超混沌LC振荡器模型,采用DDBEMPSO算法优化神经网络,进行对象辨识模型,控制器自适应滤波和扰动消除器自适应滤波,振幅隐蔽调制超混沌同步保密通信仿真,仿真表明,该同步系统可以真实地实现对信号的保密通信传输。
In recent years, chaos are widely studied and applied in secure communication and other fields , because of its characters of sensitive to initial conditions, similar to noise and continuous, wide-band frequency spectrum. However, the theory of chaotic control and synchronization is still very unripe presently, and until now there are a lot of problems on theory and technology unsolved. Considering some problems existing in the studies of chaotic synchronization at present , the problems of chaotic synchronization on theory, approaches and application, etc are discussed in this paper, with the continuous and discrete chaotic systems as the objects. The main purpose is to provide theory approaches and expand theory foundation for chaotic synchronization and its application.
Firstly, considering particle swarm optimization (PSO) algorithm has the disadvantage of easy getting into premature trap, the modified particle swarm optimization (MPSO) algorithm and bee evolution modifying particle swarm optimization (BEMPSO) algorithm were given in this paper. Five typical testing functions is used to analyze and test it using the different particle swarm optimization algorithm . The results are analysed and contrasted , BEMPSO has very good convergence. It also lays an effective theoretical foundation for the studies of chaotic system synchronization in the latter chapters.
Secondly, using delamination delivery bee evolution modifying particle swarm optimization (DDBEMPSO) algorithm train artificial neural network for modeling continuous and discrete chaotic systems. Then gives training algorithms of DDBEMPSO based on RBFNN and based on CNN. Through the continuous and discrete chaotic mapping simulation , the simulating results indicates the improved method can impove search efficiency , prevent premature and realize global optimization effectively.
Thirdly, in allusion to chaos asynchronization issues caused by channel noise infuenceing chaos signal, design an adaptive inverse controller to cancel disturbance and noise in chaos synchronization system according to the adaptive inverse theory. Adaptive inverse control canceling noise in signals has optimality , it is very much suitable for the application in chaos synchronization . The continuous and discrete chaotic systems synchronization disturbed by noises is investigated using this method. By the comparative digital simulation using of DDBEMPSO algorithm optimizing RBFNN and CNN to identify and control discrete chaotic systems synchronization, it concludes that the latter is better.
Finally, the synchronization approaches above are applied in secure communication by amplitude masking modulation and the general procedures of discrete chaotic systems synchronization controlled adaptive inverse by amplitude masking modulation is discribed. Study of simulation is carried out by using Logistic mapping and Lorenz chaos system as example . It mainly interprets hyperchaotic synchronization secure communication and analyses 4-dimensional hyperchaotic LC oscillator model , using DDBEMPSO algorithm optimizes artificial neural network , identifies object model and have adaptive filtering in controller and disturbance canceller . Through sumulation of hyperchaotic synchronization secure communication by amplitude masking modulation , the simulation result shows the synchronization system accomplish the signal secure communication transmission truly.
首先,针对粒子群优化算法(PSO)易陷入早熟陷阱的缺点,本文提出改进型粒子群优化算法(MPSO)和蜜蜂进化型粒子群优化算法(BEMPSO)。本文对五个典型的测试函数分别用不同的粒子群优化算法进行了优化仿真实验,并对实验结果进行了比较和分析,得出BEMPSO具有很好的收敛性。这些理论的研究将为本文以后章节的研究提供有力的研究依据。
其次,为了实现连续和离散混沌系统建模,将分层递阶蜜蜂进化型粒子群优化(DDBEMPSO)算法用于神经网络训练,给出了基于DDBEMPSO的RBF神经网络学习算法的设计方法和基于DDBEMPSO的混沌神经网络学习算法的设计方法。通过连续和离散混沌映射时间序列预测的仿真实验,得出分层递阶蜜蜂进化型粒子群优化方法提高了搜索效率,克服了早熟现象,提高了收敛性,取得了较好的仿真结果。
再次,针对混沌信号受到信道噪声的影响,难以很好的达到同步问题,基于自适应逆的原理设计了自适应逆控制器,引入到混沌同步,对系统中存在的扰动和噪声进行了消除,取得了很好的效果。自适应逆控制对于消除信号中的噪声具有最优性,非常适合在混沌同步中应用。并采用此方法对噪声干扰的离散混沌系统和连续混沌系统同步仿真研究,对比利用DDBEMPSO优化RBFNN和CNN用于辨识和控制离散混沌系统同步数字仿真,可知对离散混沌系统来说,采用CNN结构构造辨识器和控制器比采用RBFNN结构构造辨识器和控制器性能更优越。
最后,详细地介绍了基于混沌同步的振幅隐蔽调制保密通信原理,并对自适应逆控制的振幅隐蔽调制离散混沌同步步骤加以说明。分别以Logistic映设和Lorenz连续混沌系统为例进行仿真研究。重点阐述了超混沌同步的保密通信,分析四维超混沌LC振荡器模型,采用DDBEMPSO算法优化神经网络,进行对象辨识模型,控制器自适应滤波和扰动消除器自适应滤波,振幅隐蔽调制超混沌同步保密通信仿真,仿真表明,该同步系统可以真实地实现对信号的保密通信传输。
In recent years, chaos are widely studied and applied in secure communication and other fields , because of its characters of sensitive to initial conditions, similar to noise and continuous, wide-band frequency spectrum. However, the theory of chaotic control and synchronization is still very unripe presently, and until now there are a lot of problems on theory and technology unsolved. Considering some problems existing in the studies of chaotic synchronization at present , the problems of chaotic synchronization on theory, approaches and application, etc are discussed in this paper, with the continuous and discrete chaotic systems as the objects. The main purpose is to provide theory approaches and expand theory foundation for chaotic synchronization and its application.
Firstly, considering particle swarm optimization (PSO) algorithm has the disadvantage of easy getting into premature trap, the modified particle swarm optimization (MPSO) algorithm and bee evolution modifying particle swarm optimization (BEMPSO) algorithm were given in this paper. Five typical testing functions is used to analyze and test it using the different particle swarm optimization algorithm . The results are analysed and contrasted , BEMPSO has very good convergence. It also lays an effective theoretical foundation for the studies of chaotic system synchronization in the latter chapters.
Secondly, using delamination delivery bee evolution modifying particle swarm optimization (DDBEMPSO) algorithm train artificial neural network for modeling continuous and discrete chaotic systems. Then gives training algorithms of DDBEMPSO based on RBFNN and based on CNN. Through the continuous and discrete chaotic mapping simulation , the simulating results indicates the improved method can impove search efficiency , prevent premature and realize global optimization effectively.
Thirdly, in allusion to chaos asynchronization issues caused by channel noise infuenceing chaos signal, design an adaptive inverse controller to cancel disturbance and noise in chaos synchronization system according to the adaptive inverse theory. Adaptive inverse control canceling noise in signals has optimality , it is very much suitable for the application in chaos synchronization . The continuous and discrete chaotic systems synchronization disturbed by noises is investigated using this method. By the comparative digital simulation using of DDBEMPSO algorithm optimizing RBFNN and CNN to identify and control discrete chaotic systems synchronization, it concludes that the latter is better.
Finally, the synchronization approaches above are applied in secure communication by amplitude masking modulation and the general procedures of discrete chaotic systems synchronization controlled adaptive inverse by amplitude masking modulation is discribed. Study of simulation is carried out by using Logistic mapping and Lorenz chaos system as example . It mainly interprets hyperchaotic synchronization secure communication and analyses 4-dimensional hyperchaotic LC oscillator model , using DDBEMPSO algorithm optimizes artificial neural network , identifies object model and have adaptive filtering in controller and disturbance canceller . Through sumulation of hyperchaotic synchronization secure communication by amplitude masking modulation , the simulation result shows the synchronization system accomplish the signal secure communication transmission truly.
引文
[1]方锦清,赵耿,罗晓曙.混沌保密通信应用研究的进展.广西师范大学学报(自然科学版).2002,20(1):6-18页
[2]方锦清.非线性系统中混沌控制方法、同步原理及其应用前景(一),物理学进展.1996,16(1):1-70页
[3]方锦清.非线性系统中混沌控制方法、同步原理及其应用前景(二),物理学进展.1996,16(2):137-196页
[4]方锦清.驾驭混沌与发展高新技术.原子能出版社,2002:1-180页
[5]Ott E.,Grebogi C.and Yorke J.A.Controlling chaos.Phys Rev Lett.1990,64(8):1196-1199P
[6]Pecora L.M.,Carroll T.L.Synchronization in chaotic systems.Phys Rev Lett.1990,64(8):821-824P
[7]Boccaletti S.,Grebogi C.,Lai Y.C.,et al.The Control of Chaos:theory and application.Physics Reports.2000,329:103-197P
[8]Grebogi,C.,Lai Y.C.Controlling chaotic dynamical systems.Systems &Control Letters.1997,31:307-312P
[9]Grebogi,C.,Lai,Y.C.,Hayes,S..Control and Applications of Chaos.International Journal Bif And Chaos.1997,7:2175-2198P
[10]曹建福,韩崇昭,方洋旺.非线性系统理论及应用.西安交通大学出版社,2001:73-83页
[11]方锦清.非线性控制与混沌控制论:略谈与现代控制论的结合.自然杂志.1998,20(3):147-152页
[12]P.G.Vaidya.Monitoring and speeding up chaotic synchronization.Chaos,Solitons and Fractals.2003,17:433-439 P
[13]吴祥兴等编著.混沌学导论.上海科技文献出版社,1996:120-143页
[14]方锦清.超混沌,混沌的控制与同步.科技导报(北京).1996(4):6-8页
[15]张学义.混沌同步及其在通信中的应用研究.哈尔滨工程大学博士学位 论文.2001:l-10页,57-60页
[16] Kennedy J., Eberhart R. C. , Particle swarm opti-mization. Proceedings of IEEE International Conference on Neural Network. Piscataway, NJ: IEEE Press, 1995:1942-1948P
[17] Widrow B. Adaptive inverse control. 2nd IFAC Workshop on Adaptive Systems in Control and Signal Processing, Lund,1986:1-5P
[18] Poincare H. The Value of Science: Essential Writings of Henri Poincare.Modern Library, 2001:442-548P
[19] Kolmogorov, A.N., On conservation of conditionally periodic motions for a small change in Hamiltonian's function, Dokl. Akad. Nauk SSSR,1954,98:525-530P
[20] Arnold, V.I., Proof of A.N. Kolmogorov's theorem on the preservation of quasi-periodic motions under small perturbations of Hamiltonian, Russian Math. Surveys, 1963,18:9-36P
[21] Moser, J., On invariant curves of area preserving mapping of an annulus,Nachr. Akad.Wiss.Gottingen Math.-Phys.,K1, 1962,2:1-20P
[22] Lorenz, N. Edward: Deterministic non-periodic flows. Journal of Atmospheric Science, 1963,20(2):130-141P
[23] Ruelle D., Takens F., On the nature of turbulence. Commun Math Phys,1971,20(1):167-192P
[24] Li T. Y, Yorke J. A.,Period three implies chaos.American Mathematical Monthly, 1975, 82(10):985-992P
[25] Packard N.H., Crutchfield J. P., Farmer J. D.,et al. Geometry from a time series, Phys.Rev. Lett., 1980,45(9):712-716P
[26] Takens F.,Detecting strange attractors in fluid turbulence.In D.Rand and L.S.Young,editors,Dynamical Systems and Turbulence.Berlin, Springer Verlag, 1981:366-381P
[27] Gukenheimer J. , Holmes P., Nonlinear Oscillations, Dynamical Systems,and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983
[28] Ford J. Directions in classical chaos in Directions in chaos, Vol. 1, 1-16, World Sci.Publishing,Singapore,1987
[29]Hao B.L.,Elementary Symbolic Dynamics and Chaos in Dissipative System.World Scientific,Singapore,1989
[30]Carroll T.L.,Recora L.M.,Synchronization in chaotic circuits.IEEE Trans.on CAS,1991,CAS-38(4):453-456P
[31]Li T.Y,Yorke J.A.,Period three implies chaos.The American Mathematical Monthly,1975,82(10):985-992P
[32]Devancy R.L.,An introduction to chaotic dynamical system,Addison-Wesley Publishing Company,1989
[33]Lorenz,E.N.,The Essence of Chaos,Washington:USA University of Washington Press,1993
[34]Kolcarev L.,Parlitz U.General approach for chaotic synchronization with applications to communication.Phys.Rev.Lett.,1995,74(1):65-68P
[35]Gaponov-Grekhov A.V.,Rabinovich M.I.,Nonlinear dynamics of nonequilibrium media:structures and turbulence,Soviet Physics Uspekhi,1987,30(5):433-434P
[36]Winful H.G.,Rahman L.,Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers.Phys.Rev.Lett.,1990,65(13):1575-1578P
[37]黄润生.混沌及其应用.武汉大学出版社,2000:291-295页
[38]戴旭初,徐佩霞.混沌同步的方法及其若干问题.电路与系统学报.1998,3(1):44-51页
[39]Bu S.,L.,Wang Sh.,Ye H.,Q..An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems.Physica D 164,2002:45-52P
[40]Michele B.,Donato C.,Synchronization of hyper-chaoic circuits via continuous feedback control with application to secure communication.Int.J.Bifurcation and Chaos,1998,8(9):2031-2040P
[41]成雁翔,王光瑞.用非线性反馈实现混沌的同步化.物理学报.1995,44(9):1383-1389页
[42]方天华.实现混沌同步的非线性变量反馈控制法.原子能科学技术.1998,32(1):28页
[43]方天华.用非线性反馈函数法研究蔡电子线路的混沌同步.原子能科学技术.1997,31(6):488-492页
[44]陈明杰.连续混沌系统同步及应用研究.哈尔滨工程大学博士学位论文.2005:10-21,57-60页
[45]陈从颜,宋文忠.一类非线性反馈混沌系统分析和同步控制.控制与决策.2002,17(1):49-52页
[46]宋本祥,孙鹏.混沌同步化的非线性反馈方法.鞍山师范学院学报(综合版).1997,18(2):26-28页
[47]Duan,C.K,Yang,S.S.,Min W.L.et al,,Feedback-Control to Realize and Stabilize Chaos Synchronization.Chaos,Solitons & Fractals.1998,9(6):921-929P
[48]Zhou T.Sh.,L(u|¨) J.H.,Chen G.R.et al,Synchronization stability of three chaotic systems with linear coupling.Physics Letters A 301,2002:231-240P
[49]L(u|¨) J.H.,Zhou T.Sh.,Zhang S.Ch.,Chaos synchronization between linearly coupled chaotic systems.Chaos,Solitons and Fractals 14,2002:529-541P
[50]卢俊国,汪小帆,王执铨.连续时间混沌系统控制与同步的状态反馈方法.控制与决策.2001,16(4):44-47页
[51]宋杨.混沌同步化的线性反馈理论.大连铁道学院学报.1998,19(4):9-12页
[52]Kouomou Y.C.,Woafo P.,Stability and optimization of chaos synchronization through feedback coupling with delay.Physics Letters A 298,2002:18-28P
[53]Huang,Zh.,X.,Ruan,J.Synchronization of chaotic systems by linear feedback controller.Communications in Nonlinear Science and Numerical Simulation.1998,3(1):27-30P
[54]Nijmeijer H.,Mareels I.M.Y.,An observer looks at synchro-nization.IEEE Transactions on Circuits and Systems Ⅰ:Fundamental Theory and Applications,1997,44(10):882-890P
[55]蒋国平,王锁平.基于状态观测器的超混沌同步方法.电子学报.2000,28(1):108-110页
[56]杨绿溪,李克.用于混沌同步的非线性观测器的稳定性分析.中国科学.2001,31:355-362页
[57]Santoboni G.,Pogromsky A.Y.,Nijmeijer H.,An observer for phase synchronization of chaos.Physics Letters A 291,2001:265-273P
[58]Ercan S.,Omer M.,Umut E.Observer-based control of a class of chaotic systems.Physics Letters A 279,2001:47-55P
[59]Feki M.,Observer-based exact synchronization of ideal and mismatched chaotic systems.Physics Letters A 309,2003:53-60P
[60]Bai E.W.,Lonngren K.E.,Ucar A.,Secure communication via multiple parameter modulationin a delayed chaotic system,Chaos,Solitons and Fractals,2005,23:1071-1076P
[61]Feki M.,Robert B.,Observer-based chaotic synchronization in the presence of unknown inputs.Chaos,Solitons and Fractals 15,2003:831-840P
[62]Di Bernrdo M.,An Adaptive Approach to the Control and Synchronization of Continuous time chaotic System,M.J.Bifurc.Chaos.1996,6(3):557-568P
[63]Alexander L.F.,Markov A.Y.,Adaptive Synchronization of chaotic system phased on Speed gradient method and passification.IEEE Trans.on Cucuits Syst.(Ⅰ),1997,44(10):905-912P
[64]高金峰,潘秀琴,王俊昆.自适应方法控制混沌超混沌系统同步的研究.计算技术与自动化.1999,18(4):7-12页
[65]王福田,洪奕光.关于混沌系统的鲁棒和自适应同步化[J].控制理论与应用.2000,17(1):38-42页
[66]Maybhate A.,Amritkar R.,E.,Use of synchronization and adaptive control in parameter estimation from a time series.Physical Review E,1999,59(1):284-292P
[67]Dai D.,Ma X.K.,Chaos synchronization by using intermittent parametric adaptive control method.Physics Letters A 288,2001:23-28P
[68]马军.四维 L.C 振子超混沌系统的同步研究.广西师范大学硕士学位论文.2003;14-42页
[69]Yuan H.T.,Chen C.K.,Chen C.L.,Sliding mode control of chaotic systems with uncertainty.Int J Bifu and Chaos,2000,10(5):1139-1147P
[70]杨涛,张斌,邵惠鹤.滑模控制策略在具有不确定性的混沌系统同步中的应用.通信学报.2002,12(23):16-22页
[71]赵辽英.基于参数辨识的混沌同步变结构控制.杭州电子工业学院学报.2003,23(4):4-7页
[72]Li Zh.,Shi S.J.,Robust adaptive synchronization of Rossler and Chen chaotic systems via slide technique.Physics Letters A 311,2003:389-395P
[73]Xue Y.J.,Yang S.Y.,Synchronization of generalized Henon map by using adaptive fuzzy controller.Chaos,Solitons and Fractals 17,2003:717-722P
[74]He R.,Vaidya P.G.,Analysis and synthesis of synchronous periodic and chaotic systems.Phys.Rev.A,1992,46(12):7387-7392P
[75]Wang X.F.,Wang Zh.Q.,A new criterion for synchronization of coupled chaotic oscillators with application to chua's circuits.International Journal of Bifurcation and Chaos,1999,9(6):1169-1174P
[76]Jiang G.P.,A new criterion for chaos synchronization using linear state feedback control.International Journal of Bifurcation and Chaos,2003,13(8):2343-2351P
[77]Sun J.t.,Zhang Y.P.,Some simple global synchronization criterions for coupled time-varying chaotic systems Chaos,Solitons and Fractals 2004,19:93-98P
[78]Sun J.t.,Zhang Y.P.,Qiao.,Wu Q.D.,Some impulsive synchronization criterions for coupled chaotic systems via unidirectional linear error feedback approach.Chaos,Solitons and Fractals,2004,19:1049-1055P
[79]Jiang G.P.,Tang W.K.,Chen G.R.,A simple global synchronization criterion for coupled chaotic systems.Chaos,Solitons and Fractals,2003,15:925-935P
[80]Yu H.J.,Liu Y.Z.,Chaotic synchronization based on stability criterion of linear systems.Physics Letters A,2003,314:292-298P
[81]Caroll T.L.,Synchronizing chaotic systems using filtered signals.Phys Rev E.1994,50:2580-2587P
[82]苏野平,何晨,诸鸿文.CNN混沌保密通信系统抗噪声性能的增强.上海交 通大学学报.1999,33(9):1080-1084页
[83]程艳云,蒋国平.分段线性连续混沌系统的H~∞同步方法.南京邮电学院学报.2003,23(4):17-26页
[84]邱庚香,陈德海.基于小波变换的信号去噪应用.南方冶金学院学报.2003,24(4):13-16页
[85]刘汉忠,顾晓辉,刘贯领,张文.基于小波变换的声信号去噪处理方法.声学与电子工程.2003,4:11-14页
[86]刘娟花.小波分析在语音去噪中的应用.西安理工大学硕士学位论文.2004:2-42页
[87]王振国,汪恩华.小波包相关阀值去噪.石油物探.2002,41(4):400-405页
[88]江景涛,徐永建,王树英.基于小波包分析的工程图纸降噪及Matlab实现.莱阳农学院学报.2003,20(4):305-307页
[89]魏云冰,黄进,黄建华.基于小波包变换的电机测试信号去噪处理.电工技术学报.2001,16(5):64-67页
[90]袁像泉,马晓岩.基于平均阈值的小波包去噪方法研究.武汉交通科技大学学报.2000,24(2):215-217页
[91]Chua L.O.,Komuro M.,Mastsumoto T.,The double scroll family.IEEE Trans.Circuits Syst.I.1986,33(11):1073-1118P
[92]Chua L.O.,Special issue on chaotic systems.Proceedings of IEEE.1987,75(8):979-1120P
[93]Yang,S.S.,Duan,C.K.Generalized Synchronization in Chaotic Systems,Chaos,Solitons & Fractals.1998,9(10):1703-1707P
[94]彭军,廖晓峰,吴中福.混沌在保密通信中的应用研究.重庆工业高等专科学校学报.2002,17(3):1-3页
[95]翁贻方,Pei Yu.混沌同步原理及其在保密通信中的应用.北京轻工业学院学报.2001,18(1):47-55页
[96]方锦清,赵耿,罗晓曙.混沌保密通信应用研究的进展.广西师范大学学报(自然科学版).2002,20(1):6-18页
[97]Papadimitriou S.,Bezerianos A.,Bountis T.,et al.Secure communication protocols with discrete nonlinear chaotic maps.Journal of Systems Architecture 47,2001:61-72P
[98]Nan M.K.,Wong Ch.N.,Tsang K.F.,et al,Secure digital communication based on linearly synchronized chaotic maps.Physics Letters A 268,2000:61-68P
[99]Kennedy,M.P.,Kolumbam,G.,Digital communications using chaos.Signal Processing.2000,80(7):1307-1320P
[100]倪皖荪等.混沌通信.物理学进展.1996.16(3,4):645-655页
[101]Frey D.R.,Chaotic digital encoding:an approach to secure communication.IEEE Trans.CAS_Ⅱ,1993,Vol.40,No,10:660-666P
[102]张涛,高闽光,张玉春,路铁群.混沌通信的研究.光电子技术与信息.2000,13(1):26-30页
[103]Chen C.C.,Yao K.Umeno K.et al,Design of Spread-Spectrum Sequences Using Chaotic Dynamical Systems and Ergodic Theory,IEEE Transactions on Circuits and Systems-Ⅰ,2001,48(9):1110-1114P
[104]Feki M.,An adaptive chaos synchronization scheme applied to secure communication.Chaos,Solitons and Fractals 18,2003:141-148P
[105]厉小润,赵辽英,赵光宙.一种具有结构或参数失配的混沌保密通信系统.电路与系统学报.2003,8(4):25-29页
[106]刘侠等.自适应逆控制的研究综述.电气自动化.2003,25(6):5-7页
[107](美)威德罗(B.Widrow),(以色列)瓦莱斯(E.Walach).自适应逆控制.刘树棠,韩崇昭译.西安:西安交通大学出版社,2000
[108]卢志刚,吴士昌,于灵慧.非线性自适应逆控制及其应用.北京:国防工业出版社,2004
[109]刘伟,王科俊,邵克勇.一类多时滞不确定线性系统的镇定.中南大学学报.2005,36(speciall):165-168页
[110]高尚.群智能算法及其应用.中国水利水电出版社,2006:1-15页
[111]杨维.粒子群优化算法综述.中国工程科学.2004,5(6):87-94页
[112]Kassabalidis I.,El-Sharkawi M.A.,Marks R.J.,et al.Adaptive-SDR:Adaptive swarm-based distributed routing,Proc.IEEE World Congress on Computational Intelligence.Hawaii,May 2002:2878-2883P
[113]Robinson J.,Sinton S.,Rahmat-Samii Y.,Particle swarm optimization,genetic algorithm,and their hybrids:Optimization of a profiled corrugated horn antenna.IEEE Antennas Propag Soc.Int.Symp,2002,1:314-317P
[114]Yoshida H.,Kawata K.,Fukuyama Y.,et al.A Particle Swarm Optimization for Reactive Power and Voltage Control Considering Voltage Security Assessment.IEEE Transactions on Power Systems,2000,15(4):1232-1239P
[115]Fukuyama Y.,Yoshida H.A.,Particle Swarm Optimization For Reactive Power and Voltage Control in Electric Power Systems.Proceedings of Congress on Evolutionary Computation,Seoul,Korea,2001:87-93P
[116]Reynolds C.W.,Flocks,Herds,and Schools:A Distributed Behavioral Model.Computer Graphics.1987,21(4):25-34P
[117]谢晓锋,张文俊,杨之廉.微粒群算法综述.控制与决策.2003,18(2):129-134页
[118]曾建潮,介婧,崔志华.微粒子群算法.科学出版社,2004
[119]Van den Bergh F.Engelbrecht A.P.Training Product Unit Networks Using Cooperative Particle Swarm Optimizers.In Proc of the third Genetic and Evolutionary Computation Conference.San Francisco.USA.2001.Microprocessors and Microsystems.26(2002):363-371P
[120]Shi Y.,Eberhart R.C.,A modified particle swarm optimizer.In Proc.IEEE International Conference on Evolutionary Computation,Piscataway,NJ:IEEE Press.1998,b:69-73P
[121]Shi Y.,Eberhart R.C.,Empirical study of particle swarm optimization.In Proc.Congress on Evolutionary Computation,Piscataway,NJ:IEEE Service C enter.1999:1945-1950P
[122]Eberhart R.C.,Shi Y.,Comparing inertia weights and constriction factors in particle swarm optimization,in Proc.Congress Evolutionary Computation,Piscataway,NJ:IEEE Press,2000:84-88P
[123]Clerc M.,The Swarm and the Queen:towards a determinstic and adaptive particle swarm optimization,in proc.ICEC Washington,DC,1999,1951-1957P
[124]Clerc M.Kennedy J.,The particle swarm explosion,stability,and convergence in a multidimensional complex space,IEEE Trans.Evolutionary Computation,2002,6(1):58-73P
[125]Fan H.Y.,Shi Y.H.,Study of Vmax of the particle swarm optimization algorithm.Proceedings of the workshop on PSO.Indianapolis:purdue school of engineering and technology,input,2001
[126]Come D.,Dorigo M.,Glover F.,New Ideas in Optimization,London:McGraw Hill,1999:379-387P
[127]Kennedy J.,Eberhart R.C.,Shi Y.,Swarm Intelligence,San Mateo,California:Morgan Kauffman.2001
[128]Kennedy J.,The particle swarm:Social adaptation of knowledge,in Proc.International Conference on Evolutionary Computation,Piscataway,New Jersey,IEEE Press,1997:303-308P
[129]Kennedy J.,Eberhart R.C.,A discrete binary version of the particle swarm algorithm,in Proc.of the IEEE International Conference on Systems Man And Cybernetics,Piscataway,New Jersey,IEEE Press,1997:4104-4108P
[130]Kennedy J.,Minds and Cultures:Particle Swarm Implications for Beings in Sociocognitive Space,Adapative Behavior,1999,7(3):269-288P
[131]Angeline P.,Using Selection to Improve Particle Swarm Optimization.In.Proc.of IEEE Intl.Conf.on Evolutionary Computation(ICEC' 98).Anchorage.May 1998
[132]Angeline,P.,Evolutionary optimization versus particle swarm Philosophy and Performance Differences.In:Evolutionary Programming Ⅶ.1998:601-610P
[133]Van den Bergh F.,Engelbrecht A.P.,Effects of Swarm Size on Cooperative Particle Swarm Optimisers.In:Proceedings of the Genetic and Evolutionary Computation Conference(GECCO),San Francisco,USA,2001
[134]史忠科.神经网络控制理论.西安:西北工业大学出版社,1997
[135]魏海坤.神经网络的结构设计的理论与方法.北京:国防工业出版社,2005
[136]王科俊,王克成.神经网络建模、预报与控制.哈尔滨:哈尔滨工程大学出 版社,1996
[137]Aihara K.,Numajiri T.,Matsumoto G.,Structures of attractors in periodically forced neural oscillators,Physics Letters A,1986,116(7):313-317P
[138]Aihara K.,Takebe T.,Toyoda M.,Chaotic neural networks,Phys.Letters A,1990,144(6-7):333-340P
[139]Adachi.M,Aihara.K,Associative dynamics in a chaotic neural network,Neural Networks,1997,10(1):83-98P
[140]Tang M.,Wang K.J,Liu W.,A Study of fuzzy chaotic neuron and fuzzy chaotic neural network,in Proc.of the IEEE International Conference on Mechatronics Automatiaon,June,2005:890-895P
[141]Mackey M.C.,Glass,L.,Oscillation and chaos in physiological control systems.Science,1977(4300):287-289P
[142]Solak E.,Morgul O.,Ersoy U.,Observer-based control of a class of chaotic systems.Physics Letters A,2001,279(1):47-55P
[143]关新平,范正平,彭海朋等.扰动情况下基于RBF网络的混沌系统同步.物理学报.2001,50(9):1670-1674页
[144]卢志刚,于灵慧,柳晓菁等.克服扰动的混沌逆控制系统.物理学报.2002,51(10):2211-2215页
[145]于灵慧,房建成.Henon混沌同步的自适应逆控制.控制理论与应用.2005,22(4):623-626页,631页
[146]Feki M.,Robert B.,Gelle G.,et al,Secure digital communication using discrete-time chaos synchronization.Chaos,Solitons and Fractals,2003,18:881-890P
[147]关新平,何宴辉,范正平.扰动情况下一类混沌系统的观测器同步.物理学报.2003,52(2):276-280页
[148]赵辽英,赵光宇,厉小润.基于Riccati方程的混沌同步方法及在保密通信中的应用.电路与系统学报.2005,10(3):5-9页
[149]TamaSeviCius A.,Namajtinas A.,Cenys A.,Simple 4D chaotic oscillator,Electronics Letters,23 May 1996,32(11):957-965P
[2]方锦清.非线性系统中混沌控制方法、同步原理及其应用前景(一),物理学进展.1996,16(1):1-70页
[3]方锦清.非线性系统中混沌控制方法、同步原理及其应用前景(二),物理学进展.1996,16(2):137-196页
[4]方锦清.驾驭混沌与发展高新技术.原子能出版社,2002:1-180页
[5]Ott E.,Grebogi C.and Yorke J.A.Controlling chaos.Phys Rev Lett.1990,64(8):1196-1199P
[6]Pecora L.M.,Carroll T.L.Synchronization in chaotic systems.Phys Rev Lett.1990,64(8):821-824P
[7]Boccaletti S.,Grebogi C.,Lai Y.C.,et al.The Control of Chaos:theory and application.Physics Reports.2000,329:103-197P
[8]Grebogi,C.,Lai Y.C.Controlling chaotic dynamical systems.Systems &Control Letters.1997,31:307-312P
[9]Grebogi,C.,Lai,Y.C.,Hayes,S..Control and Applications of Chaos.International Journal Bif And Chaos.1997,7:2175-2198P
[10]曹建福,韩崇昭,方洋旺.非线性系统理论及应用.西安交通大学出版社,2001:73-83页
[11]方锦清.非线性控制与混沌控制论:略谈与现代控制论的结合.自然杂志.1998,20(3):147-152页
[12]P.G.Vaidya.Monitoring and speeding up chaotic synchronization.Chaos,Solitons and Fractals.2003,17:433-439 P
[13]吴祥兴等编著.混沌学导论.上海科技文献出版社,1996:120-143页
[14]方锦清.超混沌,混沌的控制与同步.科技导报(北京).1996(4):6-8页
[15]张学义.混沌同步及其在通信中的应用研究.哈尔滨工程大学博士学位 论文.2001:l-10页,57-60页
[16] Kennedy J., Eberhart R. C. , Particle swarm opti-mization. Proceedings of IEEE International Conference on Neural Network. Piscataway, NJ: IEEE Press, 1995:1942-1948P
[17] Widrow B. Adaptive inverse control. 2nd IFAC Workshop on Adaptive Systems in Control and Signal Processing, Lund,1986:1-5P
[18] Poincare H. The Value of Science: Essential Writings of Henri Poincare.Modern Library, 2001:442-548P
[19] Kolmogorov, A.N., On conservation of conditionally periodic motions for a small change in Hamiltonian's function, Dokl. Akad. Nauk SSSR,1954,98:525-530P
[20] Arnold, V.I., Proof of A.N. Kolmogorov's theorem on the preservation of quasi-periodic motions under small perturbations of Hamiltonian, Russian Math. Surveys, 1963,18:9-36P
[21] Moser, J., On invariant curves of area preserving mapping of an annulus,Nachr. Akad.Wiss.Gottingen Math.-Phys.,K1, 1962,2:1-20P
[22] Lorenz, N. Edward: Deterministic non-periodic flows. Journal of Atmospheric Science, 1963,20(2):130-141P
[23] Ruelle D., Takens F., On the nature of turbulence. Commun Math Phys,1971,20(1):167-192P
[24] Li T. Y, Yorke J. A.,Period three implies chaos.American Mathematical Monthly, 1975, 82(10):985-992P
[25] Packard N.H., Crutchfield J. P., Farmer J. D.,et al. Geometry from a time series, Phys.Rev. Lett., 1980,45(9):712-716P
[26] Takens F.,Detecting strange attractors in fluid turbulence.In D.Rand and L.S.Young,editors,Dynamical Systems and Turbulence.Berlin, Springer Verlag, 1981:366-381P
[27] Gukenheimer J. , Holmes P., Nonlinear Oscillations, Dynamical Systems,and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983
[28] Ford J. Directions in classical chaos in Directions in chaos, Vol. 1, 1-16, World Sci.Publishing,Singapore,1987
[29]Hao B.L.,Elementary Symbolic Dynamics and Chaos in Dissipative System.World Scientific,Singapore,1989
[30]Carroll T.L.,Recora L.M.,Synchronization in chaotic circuits.IEEE Trans.on CAS,1991,CAS-38(4):453-456P
[31]Li T.Y,Yorke J.A.,Period three implies chaos.The American Mathematical Monthly,1975,82(10):985-992P
[32]Devancy R.L.,An introduction to chaotic dynamical system,Addison-Wesley Publishing Company,1989
[33]Lorenz,E.N.,The Essence of Chaos,Washington:USA University of Washington Press,1993
[34]Kolcarev L.,Parlitz U.General approach for chaotic synchronization with applications to communication.Phys.Rev.Lett.,1995,74(1):65-68P
[35]Gaponov-Grekhov A.V.,Rabinovich M.I.,Nonlinear dynamics of nonequilibrium media:structures and turbulence,Soviet Physics Uspekhi,1987,30(5):433-434P
[36]Winful H.G.,Rahman L.,Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers.Phys.Rev.Lett.,1990,65(13):1575-1578P
[37]黄润生.混沌及其应用.武汉大学出版社,2000:291-295页
[38]戴旭初,徐佩霞.混沌同步的方法及其若干问题.电路与系统学报.1998,3(1):44-51页
[39]Bu S.,L.,Wang Sh.,Ye H.,Q..An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems.Physica D 164,2002:45-52P
[40]Michele B.,Donato C.,Synchronization of hyper-chaoic circuits via continuous feedback control with application to secure communication.Int.J.Bifurcation and Chaos,1998,8(9):2031-2040P
[41]成雁翔,王光瑞.用非线性反馈实现混沌的同步化.物理学报.1995,44(9):1383-1389页
[42]方天华.实现混沌同步的非线性变量反馈控制法.原子能科学技术.1998,32(1):28页
[43]方天华.用非线性反馈函数法研究蔡电子线路的混沌同步.原子能科学技术.1997,31(6):488-492页
[44]陈明杰.连续混沌系统同步及应用研究.哈尔滨工程大学博士学位论文.2005:10-21,57-60页
[45]陈从颜,宋文忠.一类非线性反馈混沌系统分析和同步控制.控制与决策.2002,17(1):49-52页
[46]宋本祥,孙鹏.混沌同步化的非线性反馈方法.鞍山师范学院学报(综合版).1997,18(2):26-28页
[47]Duan,C.K,Yang,S.S.,Min W.L.et al,,Feedback-Control to Realize and Stabilize Chaos Synchronization.Chaos,Solitons & Fractals.1998,9(6):921-929P
[48]Zhou T.Sh.,L(u|¨) J.H.,Chen G.R.et al,Synchronization stability of three chaotic systems with linear coupling.Physics Letters A 301,2002:231-240P
[49]L(u|¨) J.H.,Zhou T.Sh.,Zhang S.Ch.,Chaos synchronization between linearly coupled chaotic systems.Chaos,Solitons and Fractals 14,2002:529-541P
[50]卢俊国,汪小帆,王执铨.连续时间混沌系统控制与同步的状态反馈方法.控制与决策.2001,16(4):44-47页
[51]宋杨.混沌同步化的线性反馈理论.大连铁道学院学报.1998,19(4):9-12页
[52]Kouomou Y.C.,Woafo P.,Stability and optimization of chaos synchronization through feedback coupling with delay.Physics Letters A 298,2002:18-28P
[53]Huang,Zh.,X.,Ruan,J.Synchronization of chaotic systems by linear feedback controller.Communications in Nonlinear Science and Numerical Simulation.1998,3(1):27-30P
[54]Nijmeijer H.,Mareels I.M.Y.,An observer looks at synchro-nization.IEEE Transactions on Circuits and Systems Ⅰ:Fundamental Theory and Applications,1997,44(10):882-890P
[55]蒋国平,王锁平.基于状态观测器的超混沌同步方法.电子学报.2000,28(1):108-110页
[56]杨绿溪,李克.用于混沌同步的非线性观测器的稳定性分析.中国科学.2001,31:355-362页
[57]Santoboni G.,Pogromsky A.Y.,Nijmeijer H.,An observer for phase synchronization of chaos.Physics Letters A 291,2001:265-273P
[58]Ercan S.,Omer M.,Umut E.Observer-based control of a class of chaotic systems.Physics Letters A 279,2001:47-55P
[59]Feki M.,Observer-based exact synchronization of ideal and mismatched chaotic systems.Physics Letters A 309,2003:53-60P
[60]Bai E.W.,Lonngren K.E.,Ucar A.,Secure communication via multiple parameter modulationin a delayed chaotic system,Chaos,Solitons and Fractals,2005,23:1071-1076P
[61]Feki M.,Robert B.,Observer-based chaotic synchronization in the presence of unknown inputs.Chaos,Solitons and Fractals 15,2003:831-840P
[62]Di Bernrdo M.,An Adaptive Approach to the Control and Synchronization of Continuous time chaotic System,M.J.Bifurc.Chaos.1996,6(3):557-568P
[63]Alexander L.F.,Markov A.Y.,Adaptive Synchronization of chaotic system phased on Speed gradient method and passification.IEEE Trans.on Cucuits Syst.(Ⅰ),1997,44(10):905-912P
[64]高金峰,潘秀琴,王俊昆.自适应方法控制混沌超混沌系统同步的研究.计算技术与自动化.1999,18(4):7-12页
[65]王福田,洪奕光.关于混沌系统的鲁棒和自适应同步化[J].控制理论与应用.2000,17(1):38-42页
[66]Maybhate A.,Amritkar R.,E.,Use of synchronization and adaptive control in parameter estimation from a time series.Physical Review E,1999,59(1):284-292P
[67]Dai D.,Ma X.K.,Chaos synchronization by using intermittent parametric adaptive control method.Physics Letters A 288,2001:23-28P
[68]马军.四维 L.C 振子超混沌系统的同步研究.广西师范大学硕士学位论文.2003;14-42页
[69]Yuan H.T.,Chen C.K.,Chen C.L.,Sliding mode control of chaotic systems with uncertainty.Int J Bifu and Chaos,2000,10(5):1139-1147P
[70]杨涛,张斌,邵惠鹤.滑模控制策略在具有不确定性的混沌系统同步中的应用.通信学报.2002,12(23):16-22页
[71]赵辽英.基于参数辨识的混沌同步变结构控制.杭州电子工业学院学报.2003,23(4):4-7页
[72]Li Zh.,Shi S.J.,Robust adaptive synchronization of Rossler and Chen chaotic systems via slide technique.Physics Letters A 311,2003:389-395P
[73]Xue Y.J.,Yang S.Y.,Synchronization of generalized Henon map by using adaptive fuzzy controller.Chaos,Solitons and Fractals 17,2003:717-722P
[74]He R.,Vaidya P.G.,Analysis and synthesis of synchronous periodic and chaotic systems.Phys.Rev.A,1992,46(12):7387-7392P
[75]Wang X.F.,Wang Zh.Q.,A new criterion for synchronization of coupled chaotic oscillators with application to chua's circuits.International Journal of Bifurcation and Chaos,1999,9(6):1169-1174P
[76]Jiang G.P.,A new criterion for chaos synchronization using linear state feedback control.International Journal of Bifurcation and Chaos,2003,13(8):2343-2351P
[77]Sun J.t.,Zhang Y.P.,Some simple global synchronization criterions for coupled time-varying chaotic systems Chaos,Solitons and Fractals 2004,19:93-98P
[78]Sun J.t.,Zhang Y.P.,Qiao.,Wu Q.D.,Some impulsive synchronization criterions for coupled chaotic systems via unidirectional linear error feedback approach.Chaos,Solitons and Fractals,2004,19:1049-1055P
[79]Jiang G.P.,Tang W.K.,Chen G.R.,A simple global synchronization criterion for coupled chaotic systems.Chaos,Solitons and Fractals,2003,15:925-935P
[80]Yu H.J.,Liu Y.Z.,Chaotic synchronization based on stability criterion of linear systems.Physics Letters A,2003,314:292-298P
[81]Caroll T.L.,Synchronizing chaotic systems using filtered signals.Phys Rev E.1994,50:2580-2587P
[82]苏野平,何晨,诸鸿文.CNN混沌保密通信系统抗噪声性能的增强.上海交 通大学学报.1999,33(9):1080-1084页
[83]程艳云,蒋国平.分段线性连续混沌系统的H~∞同步方法.南京邮电学院学报.2003,23(4):17-26页
[84]邱庚香,陈德海.基于小波变换的信号去噪应用.南方冶金学院学报.2003,24(4):13-16页
[85]刘汉忠,顾晓辉,刘贯领,张文.基于小波变换的声信号去噪处理方法.声学与电子工程.2003,4:11-14页
[86]刘娟花.小波分析在语音去噪中的应用.西安理工大学硕士学位论文.2004:2-42页
[87]王振国,汪恩华.小波包相关阀值去噪.石油物探.2002,41(4):400-405页
[88]江景涛,徐永建,王树英.基于小波包分析的工程图纸降噪及Matlab实现.莱阳农学院学报.2003,20(4):305-307页
[89]魏云冰,黄进,黄建华.基于小波包变换的电机测试信号去噪处理.电工技术学报.2001,16(5):64-67页
[90]袁像泉,马晓岩.基于平均阈值的小波包去噪方法研究.武汉交通科技大学学报.2000,24(2):215-217页
[91]Chua L.O.,Komuro M.,Mastsumoto T.,The double scroll family.IEEE Trans.Circuits Syst.I.1986,33(11):1073-1118P
[92]Chua L.O.,Special issue on chaotic systems.Proceedings of IEEE.1987,75(8):979-1120P
[93]Yang,S.S.,Duan,C.K.Generalized Synchronization in Chaotic Systems,Chaos,Solitons & Fractals.1998,9(10):1703-1707P
[94]彭军,廖晓峰,吴中福.混沌在保密通信中的应用研究.重庆工业高等专科学校学报.2002,17(3):1-3页
[95]翁贻方,Pei Yu.混沌同步原理及其在保密通信中的应用.北京轻工业学院学报.2001,18(1):47-55页
[96]方锦清,赵耿,罗晓曙.混沌保密通信应用研究的进展.广西师范大学学报(自然科学版).2002,20(1):6-18页
[97]Papadimitriou S.,Bezerianos A.,Bountis T.,et al.Secure communication protocols with discrete nonlinear chaotic maps.Journal of Systems Architecture 47,2001:61-72P
[98]Nan M.K.,Wong Ch.N.,Tsang K.F.,et al,Secure digital communication based on linearly synchronized chaotic maps.Physics Letters A 268,2000:61-68P
[99]Kennedy,M.P.,Kolumbam,G.,Digital communications using chaos.Signal Processing.2000,80(7):1307-1320P
[100]倪皖荪等.混沌通信.物理学进展.1996.16(3,4):645-655页
[101]Frey D.R.,Chaotic digital encoding:an approach to secure communication.IEEE Trans.CAS_Ⅱ,1993,Vol.40,No,10:660-666P
[102]张涛,高闽光,张玉春,路铁群.混沌通信的研究.光电子技术与信息.2000,13(1):26-30页
[103]Chen C.C.,Yao K.Umeno K.et al,Design of Spread-Spectrum Sequences Using Chaotic Dynamical Systems and Ergodic Theory,IEEE Transactions on Circuits and Systems-Ⅰ,2001,48(9):1110-1114P
[104]Feki M.,An adaptive chaos synchronization scheme applied to secure communication.Chaos,Solitons and Fractals 18,2003:141-148P
[105]厉小润,赵辽英,赵光宙.一种具有结构或参数失配的混沌保密通信系统.电路与系统学报.2003,8(4):25-29页
[106]刘侠等.自适应逆控制的研究综述.电气自动化.2003,25(6):5-7页
[107](美)威德罗(B.Widrow),(以色列)瓦莱斯(E.Walach).自适应逆控制.刘树棠,韩崇昭译.西安:西安交通大学出版社,2000
[108]卢志刚,吴士昌,于灵慧.非线性自适应逆控制及其应用.北京:国防工业出版社,2004
[109]刘伟,王科俊,邵克勇.一类多时滞不确定线性系统的镇定.中南大学学报.2005,36(speciall):165-168页
[110]高尚.群智能算法及其应用.中国水利水电出版社,2006:1-15页
[111]杨维.粒子群优化算法综述.中国工程科学.2004,5(6):87-94页
[112]Kassabalidis I.,El-Sharkawi M.A.,Marks R.J.,et al.Adaptive-SDR:Adaptive swarm-based distributed routing,Proc.IEEE World Congress on Computational Intelligence.Hawaii,May 2002:2878-2883P
[113]Robinson J.,Sinton S.,Rahmat-Samii Y.,Particle swarm optimization,genetic algorithm,and their hybrids:Optimization of a profiled corrugated horn antenna.IEEE Antennas Propag Soc.Int.Symp,2002,1:314-317P
[114]Yoshida H.,Kawata K.,Fukuyama Y.,et al.A Particle Swarm Optimization for Reactive Power and Voltage Control Considering Voltage Security Assessment.IEEE Transactions on Power Systems,2000,15(4):1232-1239P
[115]Fukuyama Y.,Yoshida H.A.,Particle Swarm Optimization For Reactive Power and Voltage Control in Electric Power Systems.Proceedings of Congress on Evolutionary Computation,Seoul,Korea,2001:87-93P
[116]Reynolds C.W.,Flocks,Herds,and Schools:A Distributed Behavioral Model.Computer Graphics.1987,21(4):25-34P
[117]谢晓锋,张文俊,杨之廉.微粒群算法综述.控制与决策.2003,18(2):129-134页
[118]曾建潮,介婧,崔志华.微粒子群算法.科学出版社,2004
[119]Van den Bergh F.Engelbrecht A.P.Training Product Unit Networks Using Cooperative Particle Swarm Optimizers.In Proc of the third Genetic and Evolutionary Computation Conference.San Francisco.USA.2001.Microprocessors and Microsystems.26(2002):363-371P
[120]Shi Y.,Eberhart R.C.,A modified particle swarm optimizer.In Proc.IEEE International Conference on Evolutionary Computation,Piscataway,NJ:IEEE Press.1998,b:69-73P
[121]Shi Y.,Eberhart R.C.,Empirical study of particle swarm optimization.In Proc.Congress on Evolutionary Computation,Piscataway,NJ:IEEE Service C enter.1999:1945-1950P
[122]Eberhart R.C.,Shi Y.,Comparing inertia weights and constriction factors in particle swarm optimization,in Proc.Congress Evolutionary Computation,Piscataway,NJ:IEEE Press,2000:84-88P
[123]Clerc M.,The Swarm and the Queen:towards a determinstic and adaptive particle swarm optimization,in proc.ICEC Washington,DC,1999,1951-1957P
[124]Clerc M.Kennedy J.,The particle swarm explosion,stability,and convergence in a multidimensional complex space,IEEE Trans.Evolutionary Computation,2002,6(1):58-73P
[125]Fan H.Y.,Shi Y.H.,Study of Vmax of the particle swarm optimization algorithm.Proceedings of the workshop on PSO.Indianapolis:purdue school of engineering and technology,input,2001
[126]Come D.,Dorigo M.,Glover F.,New Ideas in Optimization,London:McGraw Hill,1999:379-387P
[127]Kennedy J.,Eberhart R.C.,Shi Y.,Swarm Intelligence,San Mateo,California:Morgan Kauffman.2001
[128]Kennedy J.,The particle swarm:Social adaptation of knowledge,in Proc.International Conference on Evolutionary Computation,Piscataway,New Jersey,IEEE Press,1997:303-308P
[129]Kennedy J.,Eberhart R.C.,A discrete binary version of the particle swarm algorithm,in Proc.of the IEEE International Conference on Systems Man And Cybernetics,Piscataway,New Jersey,IEEE Press,1997:4104-4108P
[130]Kennedy J.,Minds and Cultures:Particle Swarm Implications for Beings in Sociocognitive Space,Adapative Behavior,1999,7(3):269-288P
[131]Angeline P.,Using Selection to Improve Particle Swarm Optimization.In.Proc.of IEEE Intl.Conf.on Evolutionary Computation(ICEC' 98).Anchorage.May 1998
[132]Angeline,P.,Evolutionary optimization versus particle swarm Philosophy and Performance Differences.In:Evolutionary Programming Ⅶ.1998:601-610P
[133]Van den Bergh F.,Engelbrecht A.P.,Effects of Swarm Size on Cooperative Particle Swarm Optimisers.In:Proceedings of the Genetic and Evolutionary Computation Conference(GECCO),San Francisco,USA,2001
[134]史忠科.神经网络控制理论.西安:西北工业大学出版社,1997
[135]魏海坤.神经网络的结构设计的理论与方法.北京:国防工业出版社,2005
[136]王科俊,王克成.神经网络建模、预报与控制.哈尔滨:哈尔滨工程大学出 版社,1996
[137]Aihara K.,Numajiri T.,Matsumoto G.,Structures of attractors in periodically forced neural oscillators,Physics Letters A,1986,116(7):313-317P
[138]Aihara K.,Takebe T.,Toyoda M.,Chaotic neural networks,Phys.Letters A,1990,144(6-7):333-340P
[139]Adachi.M,Aihara.K,Associative dynamics in a chaotic neural network,Neural Networks,1997,10(1):83-98P
[140]Tang M.,Wang K.J,Liu W.,A Study of fuzzy chaotic neuron and fuzzy chaotic neural network,in Proc.of the IEEE International Conference on Mechatronics Automatiaon,June,2005:890-895P
[141]Mackey M.C.,Glass,L.,Oscillation and chaos in physiological control systems.Science,1977(4300):287-289P
[142]Solak E.,Morgul O.,Ersoy U.,Observer-based control of a class of chaotic systems.Physics Letters A,2001,279(1):47-55P
[143]关新平,范正平,彭海朋等.扰动情况下基于RBF网络的混沌系统同步.物理学报.2001,50(9):1670-1674页
[144]卢志刚,于灵慧,柳晓菁等.克服扰动的混沌逆控制系统.物理学报.2002,51(10):2211-2215页
[145]于灵慧,房建成.Henon混沌同步的自适应逆控制.控制理论与应用.2005,22(4):623-626页,631页
[146]Feki M.,Robert B.,Gelle G.,et al,Secure digital communication using discrete-time chaos synchronization.Chaos,Solitons and Fractals,2003,18:881-890P
[147]关新平,何宴辉,范正平.扰动情况下一类混沌系统的观测器同步.物理学报.2003,52(2):276-280页
[148]赵辽英,赵光宇,厉小润.基于Riccati方程的混沌同步方法及在保密通信中的应用.电路与系统学报.2005,10(3):5-9页
[149]TamaSeviCius A.,Namajtinas A.,Cenys A.,Simple 4D chaotic oscillator,Electronics Letters,23 May 1996,32(11):957-965P