不确定混沌系统的控制与同步方法研究
摘要
近年来,混沌控制与同步方法的研究有了很大的发展,不仅在理论上不断完善,而且在非线性电路、保密通讯、激光、等离子体和人体生命科学等领域取得了初步的成果并展现出十分诱人的应用前景。混沌实验系统建模的不确定性是混沌的同步所必须考虑的,其中控制方向未知又是不确定性处理中难度较大的一种情况。
本文以不确定混沌系统的Nussbaum增益同步为研究主线,主要进行了以下内容研究：1.增益受限与控制受限情况下的Nussbaum增益控制问题；2.不确定驱动-响应混沌系统的自适应同步问题；3.增益受限混沌系统的Nussbaum增益与非线性滑模复合同步问题；4.参数未知情况下的混沌系统受限Nussbaum增益同步问题。
围绕上述问题展开的具体研究内容包括：
1.对Nussbaum增益基本理论进行了深入研究,提出受限Nussbaum增益控制方法。
(1)针对传统Nussbaum增益算法存在的初始段控制量过大与增益过大问题,提出增益受限与输入受限的Nussbaum增益算法的概念。
(2)针对一阶控制方向未知系统,研究了增益受限与输入受限情况下的Nussbaum增益控制规律,分别对Nussbaum增益控制算法面临的高增益与控制量饱和威胁,提出了相应的控制策略。
2.对存在参数与未知函数不确定情况下的驱动-响应混沌系统进行自适应同步研究,提出了三种自适应同步策略。
(1)基于有界不确定的假设,采用自适应算法对不确定的界进行估计,结合PID控制的优点,研究了不确定混沌系统的自适应PID同步算法；
(2)进一步简化上述有关界条件的假设,采用鲁棒控制算法完成对不确定非线性函数的补偿,采用自适应算法完成未知参数的估计,提出了一类不确定混沌系统的鲁棒自适应同步算法；
(3)基于线性系统极点反馈的思想,利用混沌系统有界性提出极点自调节同步策略,该设计不需要驱动响应系统的精确结构与不确定形式,能够广泛应用于各类混沌系统的同步中。在此基础知识,对三种控制策略的同步精度问题进行了对比与改进研究。
3.对增益受限要求下的不确定混沌系统进行非线性滑模与Nussbaum增益复合同步研究。
(1)为了进一步提高同步精度以满足Nussbaum控制算法的匹配需要,提出了两类非线性滑模的构造设计方法,针对两类非线性滑模,分别设计了常系数同步律与自适应同步律,并进行了比较研究。
(2)针对系统对大误差增益过高而对小误差的反映迟钝的问题,提出了变增益非线性滑模自适应同步算法,能够进一步提高同步精度并避免控制算法增益过高。
(3)在此基础之上,研究了非线性滑模同步与增益受限Nussbaum控制算法的匹配结合,解决了方向未知与增益受限情况下的不确定系统同步问题。
4.控制方向未知与参数未知情况下的增益受限与控制受限Nussbaum增益同步研究。
(1)针对不存在控制方向未知的简单情况,研究了参数未知混沌系统的参数自适应同步问题,取得了较好的同步效果。
(2)针对控制方向未知的复杂情况,尤其是在增益受限的约束条件下,设计了参数未知混沌系统的增益受限Nussbaum增益同步算法,从理论上保证了对Nussbaum增益约束。同时仿真结果也表明了该Nussbaum增益能够满足预定的增益限制要求。
(3)针对存在控制方向未知与参数未知情况,考虑增益受限与控制量受饱和限制双重约束的复杂情况,提出了参数自适应同步与输入受限Nussbaum增益控制算法的匹配与复合控制问题。仿真结果表明了本文算法能够保证对传统Nussbaum增益算法的增益与控制约束。
综上所述,本文考虑了控制方向未知、系统可用增益有限以及控制输入饱和等复杂情况下的不确定混沌同步问题,增大了同步系统的抗干扰能力,为混沌保密通信的实际应用拓宽了道路。
In recent years, one can see some great developments in the area of chaos control and synchronization methods, not only some improvements in theoretical concern, but also many successful applications in the area of nonlinear circuits, security communications, laser, plasma, and bioscience, etc, which exhibits enormous and exciting application prospects. It is also necessary to consider the uncertainties caused by modeling a chaotic system in laboratory, where unknown control direction is one of the most difficult uncertainties that are hard to solve with common adaptive methods.
Synchronization of chaotic systems with Nussbaum gain method is the main line of our research and it contains the following part. The first part is about the Nussbaum gain control problem for the situation that the controller with limit gain or limit control input. The second part is about the adaptive synchronization problem of uncertain driven-response system. The third part is about the nonlinear sliding mode synchronization of chaotic systems with limit Nussbaum gain method.
The fourth part is about the limit Nussbaum gain synchronization of chaotic system with uncertain parameters.
The main research is surrounded with the above context and it can be expended as follows:
First, some basic Nussbaum gain theories are studied and a limit Nussbaum gain control method is proposed.
(1)With common Nussbaum gain method, the initial control and the gain of the controller sometimes is too big and over the reasonable scope. The concepts of limit gain Nussbaum algorithm and limit input Nussbaum algorithm are proposed respectively to solve the problem.
(2) For a simple one order system with unknown control direction, the Nussbaum gain method is studied for the special situations with limit gain or limit input, and two strategies are proposed to cope with the high gain and saturation threatens respectively.
Second, a kind of adaptive synchronization for uncertain driven and response system with unknown parameters is studied and three adaptive strategies are proposed.
(1) Based on the assumption that all uncertainties are bounded, adaptive method is used to estimate the bounds of uncertainties. Integrated with the advantage of PID control, a kind of adaptive PID algorithm is studied and applied in synchronization of uncertain chaotic systems.
(2) With a further simplification of the above assumption, a kind of robust algorithm is used to compensate the uncertain nonlinear functions. With all unknown parameters estimated by adaptive method, a robust adaptive synchronization is proposed for uncertain chaotic systems.
(3) Based on the concept of poles feedback in linear systems, a kind of synchronization method with adaptive poles is studied with the use of boundless characteristics of chaotic systems. It is unnecessary to known the accurate structure and forms of uncertainties with this design method. Also, some compare improvement for the above three methods are done.
Third, the hybrid synchronization with nonlinear sliding mode method and Nussbaum gain method is researched for uncertain chaotic systems with limit gain.
(1) Two kinds of construction methods for nonlinear sliding mode are proposed to improve the accuracy of synchronization such that it can satisfied the match condition of Nussbaum gain algorithm. Also, adaptive synchronization laws with constant coefficients or adaptive coefficients are designed respectively.
(2) For some chaotic synchronization systems, if choose a small a gain, the response speed is very slow for the situation with a small error; but if choose a big gain, the gain is viewed too high for the situation with big errors. A kind of variety gain synchronization with nonlinear sliding mode is proposed to solve the problem. So with this method, the accuracy of synchronization can be improved and also the high gain feedback problem can be avoided.
(3) Based on above research work, the match of limit Nussbaum gain method and nonlinear sliding mode synchronization is researched. And both the unknown control direction and limit gain problem are solved for the synchronization of uncertain chaotic systems.
At last, the synchronization of chaotic systems with both unknown control direction and unknown parameters is researched with the restriction that the gain of the system is limit or the input of the system is limit.
(1) For the simple situation that there is no unknown control direction, a kind of synchronization with adaptive algorithm for unknown parameters is studied and good performance is achieved.
(2) For the complex situation with unknown control directions, especially with the requirement that the gain of control system is limit, a kind of limit gain Nussbaum synchronization method is proposed for chaotic systems with unknown parameters and unknown control directions. So the Nussbaum gain is guaranteed to be limit in theory. Also, simulation results show that the Nussbaum gain can satisfy to the desired limitation.
(3) Consider the requirement that both the gain and the actuator of the system are limited, a kind of hybrid synchronization with limit input Nussbaum gain and adaptive algorithm, is proposed for chaotic systems with both unknown control directions and unknown parameters. Simulation results testify that the proposed strategy can guarantee the limitation for Nussbaum gain and input.
Above all, synchronizations of uncertain chaotic systems with some complex situations are studied, such as unknown control direction situation; the available gain of the synchronization system is limit or actuator saturation problem. All of the proposed methods make the synchronization of chaotic systems have a strong stability under some bad conditions such as there exist big disturbances. It also provides a solid base for the application of chaotic systems in secure communication.
本文以不确定混沌系统的Nussbaum增益同步为研究主线,主要进行了以下内容研究：1.增益受限与控制受限情况下的Nussbaum增益控制问题；2.不确定驱动-响应混沌系统的自适应同步问题；3.增益受限混沌系统的Nussbaum增益与非线性滑模复合同步问题；4.参数未知情况下的混沌系统受限Nussbaum增益同步问题。
围绕上述问题展开的具体研究内容包括：
1.对Nussbaum增益基本理论进行了深入研究,提出受限Nussbaum增益控制方法。
(1)针对传统Nussbaum增益算法存在的初始段控制量过大与增益过大问题,提出增益受限与输入受限的Nussbaum增益算法的概念。
(2)针对一阶控制方向未知系统,研究了增益受限与输入受限情况下的Nussbaum增益控制规律,分别对Nussbaum增益控制算法面临的高增益与控制量饱和威胁,提出了相应的控制策略。
2.对存在参数与未知函数不确定情况下的驱动-响应混沌系统进行自适应同步研究,提出了三种自适应同步策略。
(1)基于有界不确定的假设,采用自适应算法对不确定的界进行估计,结合PID控制的优点,研究了不确定混沌系统的自适应PID同步算法；
(2)进一步简化上述有关界条件的假设,采用鲁棒控制算法完成对不确定非线性函数的补偿,采用自适应算法完成未知参数的估计,提出了一类不确定混沌系统的鲁棒自适应同步算法；
(3)基于线性系统极点反馈的思想,利用混沌系统有界性提出极点自调节同步策略,该设计不需要驱动响应系统的精确结构与不确定形式,能够广泛应用于各类混沌系统的同步中。在此基础知识,对三种控制策略的同步精度问题进行了对比与改进研究。
3.对增益受限要求下的不确定混沌系统进行非线性滑模与Nussbaum增益复合同步研究。
(1)为了进一步提高同步精度以满足Nussbaum控制算法的匹配需要,提出了两类非线性滑模的构造设计方法,针对两类非线性滑模,分别设计了常系数同步律与自适应同步律,并进行了比较研究。
(2)针对系统对大误差增益过高而对小误差的反映迟钝的问题,提出了变增益非线性滑模自适应同步算法,能够进一步提高同步精度并避免控制算法增益过高。
(3)在此基础之上,研究了非线性滑模同步与增益受限Nussbaum控制算法的匹配结合,解决了方向未知与增益受限情况下的不确定系统同步问题。
4.控制方向未知与参数未知情况下的增益受限与控制受限Nussbaum增益同步研究。
(1)针对不存在控制方向未知的简单情况,研究了参数未知混沌系统的参数自适应同步问题,取得了较好的同步效果。
(2)针对控制方向未知的复杂情况,尤其是在增益受限的约束条件下,设计了参数未知混沌系统的增益受限Nussbaum增益同步算法,从理论上保证了对Nussbaum增益约束。同时仿真结果也表明了该Nussbaum增益能够满足预定的增益限制要求。
(3)针对存在控制方向未知与参数未知情况,考虑增益受限与控制量受饱和限制双重约束的复杂情况,提出了参数自适应同步与输入受限Nussbaum增益控制算法的匹配与复合控制问题。仿真结果表明了本文算法能够保证对传统Nussbaum增益算法的增益与控制约束。
综上所述,本文考虑了控制方向未知、系统可用增益有限以及控制输入饱和等复杂情况下的不确定混沌同步问题,增大了同步系统的抗干扰能力,为混沌保密通信的实际应用拓宽了道路。
In recent years, one can see some great developments in the area of chaos control and synchronization methods, not only some improvements in theoretical concern, but also many successful applications in the area of nonlinear circuits, security communications, laser, plasma, and bioscience, etc, which exhibits enormous and exciting application prospects. It is also necessary to consider the uncertainties caused by modeling a chaotic system in laboratory, where unknown control direction is one of the most difficult uncertainties that are hard to solve with common adaptive methods.
Synchronization of chaotic systems with Nussbaum gain method is the main line of our research and it contains the following part. The first part is about the Nussbaum gain control problem for the situation that the controller with limit gain or limit control input. The second part is about the adaptive synchronization problem of uncertain driven-response system. The third part is about the nonlinear sliding mode synchronization of chaotic systems with limit Nussbaum gain method.
The fourth part is about the limit Nussbaum gain synchronization of chaotic system with uncertain parameters.
The main research is surrounded with the above context and it can be expended as follows:
First, some basic Nussbaum gain theories are studied and a limit Nussbaum gain control method is proposed.
(1)With common Nussbaum gain method, the initial control and the gain of the controller sometimes is too big and over the reasonable scope. The concepts of limit gain Nussbaum algorithm and limit input Nussbaum algorithm are proposed respectively to solve the problem.
(2) For a simple one order system with unknown control direction, the Nussbaum gain method is studied for the special situations with limit gain or limit input, and two strategies are proposed to cope with the high gain and saturation threatens respectively.
Second, a kind of adaptive synchronization for uncertain driven and response system with unknown parameters is studied and three adaptive strategies are proposed.
(1) Based on the assumption that all uncertainties are bounded, adaptive method is used to estimate the bounds of uncertainties. Integrated with the advantage of PID control, a kind of adaptive PID algorithm is studied and applied in synchronization of uncertain chaotic systems.
(2) With a further simplification of the above assumption, a kind of robust algorithm is used to compensate the uncertain nonlinear functions. With all unknown parameters estimated by adaptive method, a robust adaptive synchronization is proposed for uncertain chaotic systems.
(3) Based on the concept of poles feedback in linear systems, a kind of synchronization method with adaptive poles is studied with the use of boundless characteristics of chaotic systems. It is unnecessary to known the accurate structure and forms of uncertainties with this design method. Also, some compare improvement for the above three methods are done.
Third, the hybrid synchronization with nonlinear sliding mode method and Nussbaum gain method is researched for uncertain chaotic systems with limit gain.
(1) Two kinds of construction methods for nonlinear sliding mode are proposed to improve the accuracy of synchronization such that it can satisfied the match condition of Nussbaum gain algorithm. Also, adaptive synchronization laws with constant coefficients or adaptive coefficients are designed respectively.
(2) For some chaotic synchronization systems, if choose a small a gain, the response speed is very slow for the situation with a small error; but if choose a big gain, the gain is viewed too high for the situation with big errors. A kind of variety gain synchronization with nonlinear sliding mode is proposed to solve the problem. So with this method, the accuracy of synchronization can be improved and also the high gain feedback problem can be avoided.
(3) Based on above research work, the match of limit Nussbaum gain method and nonlinear sliding mode synchronization is researched. And both the unknown control direction and limit gain problem are solved for the synchronization of uncertain chaotic systems.
At last, the synchronization of chaotic systems with both unknown control direction and unknown parameters is researched with the restriction that the gain of the system is limit or the input of the system is limit.
(1) For the simple situation that there is no unknown control direction, a kind of synchronization with adaptive algorithm for unknown parameters is studied and good performance is achieved.
(2) For the complex situation with unknown control directions, especially with the requirement that the gain of control system is limit, a kind of limit gain Nussbaum synchronization method is proposed for chaotic systems with unknown parameters and unknown control directions. So the Nussbaum gain is guaranteed to be limit in theory. Also, simulation results show that the Nussbaum gain can satisfy to the desired limitation.
(3) Consider the requirement that both the gain and the actuator of the system are limited, a kind of hybrid synchronization with limit input Nussbaum gain and adaptive algorithm, is proposed for chaotic systems with both unknown control directions and unknown parameters. Simulation results testify that the proposed strategy can guarantee the limitation for Nussbaum gain and input.
Above all, synchronizations of uncertain chaotic systems with some complex situations are studied, such as unknown control direction situation; the available gain of the synchronization system is limit or actuator saturation problem. All of the proposed methods make the synchronization of chaotic systems have a strong stability under some bad conditions such as there exist big disturbances. It also provides a solid base for the application of chaotic systems in secure communication.
引文
[1]Hao B.L. Chaos[M]. Singapore:World Scientific,1984
[2]Hao B.L. Chaos II[M]. Singapore:World Scientific,1984
[3]Yong Wang, Kwok-Wo Wong, Xiaongfeng Liao, et al., A. new chaos-based fast image encryption algorithm[J]. Applied Soft Computing,2011(11):514-522
[4]Sivakumar B. Chaostheory in geophysics, past, present and future [J]. Chaos, Solitons & Fractals,2004,19(2):441-462
[5]关新平.混沌控制及其在保密通信中的应用[M].北京：国防工业出版社,2002.
[6]陈关荣,吕金虎Lorenz系统族的动力学分析、控制与同步[M].北京：科学出版社,2003,8.
[7]Poioncare.H科学的价值[M].北京：光明日报出版社,1988,356-38
[8]Lorenz EN. Deterministic non-periods flows. J Atmos Sci 1963;20:130-141.
[9]Ruelle D, Takens.F, On the nature of turbulence [J]. Comm.Math.Phys,1971,20:167-192.
[10]Li T Y and Yorke J A. Period three implies chaos[J]. Amer.Math.Monthly,1975,82:985-992.
[11]May R M. Simple mathematical models with very complicated dynamics[J]. Nature, 1976,261:459-463
[12]Feigenbaum M J.Quantitative universality for a class of nonlinear transformations[J]. J.Stat. Phys.,1978,19:25-52
[13]Mandelbort BB.The fractal geometry of nature[M],Califonia:W.Freeman Company,1980.
[14]Takens F. Deteming strange attractors in turbulence [J], Lecture notes in Math,1981,898: 361-381
[15]Grassberger P and Procaccia I. Measuring the strangeness of strange attractors[J]. Physica D, 1983,9:189-208
[16]Lv J.H, Chen G.R, A new chaotic attractor coined. Int J Bifurc Chaos 2002;12(3):659-61.
[17]Ott E, Grebogi C and Yorke J A. Controlling chaos[J], Phys.Rev.Lett.,1990,64:1196-1199.
[18]刘锋,穆肇骊,蔡远利等一类混沌系统的非线性反馈控制[J].控制与决策.2000,15(1)：15-18
[19]BemdaroM. An Adaptive approach to the control and synchronization of continuous time chaotic systems[J]. Int J Bifurcation and chaos.1996,6(3):557-568.
[20]GE S S, Wang C, Lee T H. Adaptive backstepping control of a class of chaotic systems[J]. Int J Bifurcation and chaos.2000,10 (5):1140-1156
[21]GE S S, Wang C, Adaptive control of uncertain Chua's circuits[J]. IEEE Trans Circuits System. 2000,47(9):1397-1402
[22]Alexander L, Fradkov, Markov A Yu. Adaptive synchronization of chaotic systems based on speed gradient method and passification[J]. IEEE Trans Circuits System 1997,44(10):905-912
[23]Dong X. Chen L. Adaptive control of the uncertain Duffing oscillator[J]. Int J Bifurcation and chaos.1997,7(7):1651-1658
[24]Tao Yang. Chun-Mei Yang and Lin-Bao Yang, A Detailed Study of Adaptive Contorl of Chaotic Systems with Unknown Parameters[J]. Dynamics and Control.1998,(8):255-267
[25]Oscar. Fuzzy control of chaos[J]. Int J Bifurcation and chaos.1998.8(8):1743-1747
[26]Liang Chen, Guanrong Chen, Lee Yang-Woo, Fuzzy modeling and adaptive control of uncertain chaotic systems[J]. Information Sciences.1999,121(1):27-37
[27]Liang Chen,Guanrong Chen.Fuzzy presictive control of uncertain chaotic Systems using time series[J].Int J Bifurcation and chaos.1999,9(40:757-767
[28]Chin Teng Lin.Controlling chaos by GA-based reinforcement learning neural network[J]. IEEE Trans On neural networks.1999,10:846-859
[29]王忠勇,蔡远利,贾冬等.混沌系统的神经网络控制[J].控制与决策.2000,15(1)：55-58
[30]Nussbaum, R. D. (1983). Some remarks on the conjecture in parameter adaptive control[J]. Systems and Control Letters,3(3),243-246
[31]MARTENSSON B. Remarks on adaptive stabilization of first order nonlinear systems[J]. Systems & Control Letters,1990,14(1):1-7
[32]RYAN E P. A universal adaptive stabilizer for a class of nonlinear systems[J]. Systems & Control Letters,1991,16(3):209-218.
[33]RYAN E P. A nonlinear universal servomechanism[J]. IEEE Trans on Automatic Control, 1994,39(4):753-761.
[34]DING Z. Adaptive control of nonlinear systems with unknown virtual control coefficients[J]. Int J of Control Signal Processing,2000,14(4):505-517.
[35]YE X, JIANG J. Adaptive nonlinear design without a priori knowledge of control directions [J]. IEEE Trans on Automatic Control,1998,43(11):1617-1621.
[36]GE Shuzhi Sam, WANG J. Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems[J]. IEEE Trans on Neural Networks,2002,13(11):1409-1419.
[37]YE X D. Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control directions[J]. Automatica,1999,35(5):929-935.
[38]Ye, X. D.,& Jiang, J. P. (1998). Adaptive nonlinear design without a prioriknowledge of control directions. IEEE Transactions on Automatic Control,43(11),1617-1621.
[39]Ge, S. S., Hong, F.,& Lee, T. H. (2004). Adaptive neural control of nonlinear time-delay system with unknown virtual control coefficients.IEEE Transactions on Systems, Man, and Cybernetics-PartB:Cybernetics,34(1),499-516.
[40]Yan Li, YangQuan Chen, When is a Mittag-Leffler function a Nussbaum function? Automatica 45 (2009) 1957-1959
[41]T.P.Zhang, S.S.Ge Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs, Automatica 43(2007) 1021-1033
[42]Yang C, Ge SS, Xiang C, Chai TY, Lee TH. Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Transactions on Neural Networks 2008; 19(11):1873-86.
[43]Weisheng Chen, Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints, ISA Transactions 48 (2009) 304-311
[44]Jagannathan S, He P. Neural-network-based state-feedback control of a nonlinear discrete-time system in nonstrict feedback form. IEEE Transactions on Neural Networks 2008;19(12):2073-2087
[45]魏春玲,王强德,武玉强,控制方向未知的高次非线性系统的鲁棒自适应控制[J].控制理论与应用,Vol.24 No.4,2007,519-525
[46]Pecora.L.M. and Carroll.T.L. Synchronization of chaotic systems. Phys.Rev. Lett, 1990A(64):821-832
[47]凌复华.混沌,随机,信息流和其它[J].力学与实践.1985,7(5)：17-20
[48]T.Kapitaniak et al. Experimental synchronization of chaos using continous control. Int.J. Bifurcation and Chaos,1999,4(2):483-488
[49]R.Roy et al. Experimental synchronization in laser chaos. Phys. Rev. Lett,1994,72(22): 3502-3505
[50]T.Sugawara, Ttachikawa. Observation of synchronization in laser chaos. Phys.Rev.Lett, 1994,72(22):3502-350
[51]Gao Ping Jing et al. A simple global synchronization criterion for coupled chaotic systems. Solitons and fractals.2003,(15):925-935
[52]Jianping Yan, Changpin Li. On synchronization of three chaotic systems. Chaos,Solitons and fracrals.2005,(23):1683-1688
[53]C.Sarasola,F.J.Torrealdea,A.D Anjou. Feedback synchronization of chaotic Systems[J]. Int.J. Bifurcation and chaos.2003,13(1):177-191
[54]M.T.Yassen.Chaos synchronization between two different chaotc systems using active control.Chaos,Solitons & Fractals.2005:23(4):131-140
[55]H.N.Agiza,M.T.Yassen. Synchronization of Rossler and Chen chaotic dynamical systems using active control.Physics Letters A.2001,(278):191-197
[56]Ming-chung Ho, Yao-Chen Hung.Synchronization of two different systems by Using generalized active control. Physics Letters A.2002,(301):424-428.
[57]Jiang G.P., Tang K.S. A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach. Int. J. Bifurcation Chaos,2002,12(10):2239-2253
[58]Bu S.L., Wang S.Q.An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems. Physica D,2002,164:45-52
[59]高金峰,罗先觉,马西奎.控制与同步连续时间混沌系统的非线性反馈方法[J].物理学报,1999,48(9)：1618-1627
[60]刘杨正,费树岷Genesio-Tesi和Coullet混沌系统之间的非线性反馈同步[J].物理学报,2005,54(8)：3486-3490
[61]陶朝海,陆景安.混沌系统的速度反馈同步[J].物理学报,2005,54(11)：5058-5061
[62]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[J].控制与决策,2001,16(4)：476-479
[63]张宇,余俊明,杜功焕.连续反馈混沌同步方式在保密通讯中的应用[J].科学同步,1998,43(17)：1831-1835
[64]Kouomou Y.C., Woafo P. Stability and optimization of Chaos synchronization through feedback coupling with delay [J]. Physics Letters A,2002,298:18-28
[65]Suykens. J.A.K, Robust nonlinear H∞ synchronization of chaotic Lur's system, IEEE Trans Circuit & System1997,44(10):891-903
[66]Michele B, Donato C. Synchronization of hyper-chaotic circuits via continuous feedback control with application to secure communication. Int. J. Bifurcation and Chaos, 1998,8(10):2031-2040
[67]Alexander L.Fradkov, A Yu.Markov. Adaptive synchronization of chaotic system phased on speed gradient method and passification. IEEE Trans on Circuit Syst.(Ⅰ),1997,44(10):905-912
[68]Young_Hoon Joo, Leang-San shieh, Guangrong Chen, Hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems, IEEE Trans on Fuzzy Syst.(Ⅰ),1999,7(4):394-408
[69]Alexander Pogromsky, Henk Nijmeijer. Observer-based robust synchronization of dynamical systems. Int,J. Bifurcation and Chaos,1998,8(11):2243-2254
[70]E.M.Elabbasy,H.N.Agiza,M.M.El-dessoky.Adaptive synchronization of lv System with uncertain parameters. Chaos,solitons and fractals.2004,(21):657-667
[71]M.T.yassen. Adaptive synchronization of Rosser and lu systems with fully uncertain patameters. Chaos,solitons and fractals.2005,(23):1527-1536
[72]Ju H.Park. Adaptive sysnchronization of Rossler system with uncertain Parameters.Chaos, solitons and fractals.2005,(22):1-6
[73]T.L. Liao.Adaptive synchronization of two Lorenz system. Chaos.solitons and fractals.1998, 9(9):1555-1561
[74]Yongguang Yu, Suochun Zhang, Adaptive backstepping synchronization of uncertain chaotic system[J]. Chaos, Solitons and Fractals 21 (2004) 643-649
[75]M.T. Yassen, Adaptive chaos control and synchronization for uncertain new chaotic dynamical system[J], Physics Letters A 350 (2006) 36-43
[76]Awad El Gohary, Rizk Yassen, Adaptive control and synchronization of a coupled dynamic system with uncertain parameters[J], Chaos, Solitons and Fractals 29 (2006) 1085-1094
[77]Qiang Jia, Adaptive control and synchronization of a new hyperchaotic system with unknown parameters [J], Physics Letters A 362 (2007) 424-429
[78]Rongwei Guo, A simple adaptive controller for chaos and hyperchaos synchronization, Physics Letters A,360 (2009) 38-53
[79]Wei Lin, Adaptive chaos control and synchronization in only locally Lipschitz systems, Physics Letters A 372 (2008) 3195-3200
[80]Jian Huang, Adaptive synchronization between different hyperchaotic systems with fully uncertain parameters, Physics Letters A 372 (2008) 4799-4804
[81]Ju H. Park, S.M. Lee, O.M. Kwon, Adaptive synchronization of Genesio-Tesi chaotic system via a novel feedback control, Physics Letters A 371 (2007) 263-270
[82]Xianyong Wu, ZhiHong Guan, Zhengping Wu, Adaptive synchronization between two different hyperchaotic systems, Nonlinear Analysis 68 (2008) 1346-1351
[83]Ming-Chung Ho, Yao-Chen Hung, Zhi-Yu Liua, I-Min Jiang, Reduced-order synchronization of chaotic systems with parameters unknown, Physics Letters A 348 (2006) 251-259
[84]Jui-Sheng Lin, Jun-Juh Yan, Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller, Nonlinear Analysis:Real World Applications,68 (2008) 1346-1351
[85]Tsung-Ying Chiang, Jui-Sheng Lin,Teh-Lu Liao, Jun-Juh Yan, Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity, Nonlinear Analysis 68 (2008) 2629-2637
[86]Her-Terng Yau, Jun-Juh Yan, Chaos synchronization of different chaotic systems subjected to input nonlinearity, Applied Mathematics and Computation 197 (2008) 775-788
[87]李聪颖,牟丽君,考虑控制受限的AWCT增益调度及其在飞航导弹控制系统中的应用,第二届机电一体化与智能材料国际会议,中国桂林,2012
[88]黄显林,葛东明,输入受限高超声速飞行器鲁棒变增益控制,第二届机电一体化与智能材料国际会议(系统工程与电子技术期刊),中国桂林,2012
[89]Wanli Guo, Shihua Chen, Hong Zhou, A simple adaptive-feedback controller for chaos synchronization, Chaos, Solitons and Fractals 39 (2009) 316-321
[90]Guoyuan Qi, Zengqiang Chen, Zhuzhi Yuan, Adaptive high order differential feedback control for affine nonlinear system, Chaos, Solitons and Fractals 37 (2008) 308-315
[91]Yan-Wu Wang, Changyun Wen, Yeng Chai Soh, Jiang-Wen Xiao, Adaptive control and synchronization for a class of nonlinear chaotic systems using partial system states, Physics Letters A 351 (2006)79-84
[92]邱道尹,张健.基于单神经元的自适应PID控制系统设计及仿真[J].华北水利水电学院学报,2011(1)：34-36
[93]徐峰,李东海,适应型PID控制器参数整定性能比较[J].电子技术应用,2002(6)：135-137
[94]赵建华,沈永良,一种自适应PID控制算法[J].自动化学报,2001,27(3)：417-420
[95]李亮,康铭鑫,汽车牵引力控制系统的变参数自适应PID控制[J].机械工程学报,2011,47(12)：217-224
[96]侯砚泽,董朝阳,王青,邓舞燕,不确定切换系统的鲁棒自适应控制方案[J].北京航空航天大学学报,Vol.35 Issue (4):444-448
[97]柯海森,叶旭东,钱建海,移动机器人的鲁棒自适应控制器设计[J].浙江大学学报,2006,40(7)：1127-1131
[98］关新平,唐英干,基于神经网络的混沌系统鲁棒自适应同步[J].物理学报,2001,50(11)：1127-1131
[99]王宏伟.于双和,基于Chebyshev正交神经网络的混沌系统鲁棒自适应同步[J].控制理论与应用,2009,26(10)：1100-1105
[100]方敏,王经维,一种增益可调的极点配置自校正调节器的显式和隐式算法[J].控制理论与应用,1991,8(4)：401-406
[101]单剑锋,杨立军,极点配置自校正PID调节器[J].抚顺石油学院学报,2002(1)：12-13
[102]Alban Puai Man Tsui,Antonia J. Jones, Periodic response to external stimulation of a chaotic neural network with delayed feedback[J]. International journal of bifurcation and chaos in applied sciences and engineering,1999,9(4):322-329
[103]程丽,彭建华,极点配置法确定超混沌系统同步与控制的条件[J].广西师范大学学报,2002(1)：34-36
[104]Haitao Yu, Jiang Wang, Bin Deng, Adaptive backstepping sliding mode control for chaos synchronization of two coupled neurons in the external electrical stimulation [J]. Commun Nonlinear Sci Numer Simulat 17 (2012) 1344-1354
[105]Chao-Lin Kuo, Design of a fuzzy sliding-mode synchronization controller for two different chaos systems, Computers and Mathematics with Applications 61 (2011) 2090-2095
[106]Her-Terng Yau, Design of adaptive sliding mode controller for chaos synchronization with uncertainties, Chaos, Solitons and Fractals 22 (2004) 341-347
[107]Her-Terng Yau, Jun-Juh Yan, Chaos synchronization of different chaotic systems subjected to input nonlinearity, Applied Mathematics and Computation 197 (2008) 775-788
[108]Jui-Sheng Lin, Jun-Juh Yan,, Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller, Nonlinear Analysis:Real World Applications,68 (2008) 1346-1351
[109]Tsung-Ying Chiang, Jui-Sheng Lin Teh-Lu Liao, Jun-Juh Yan, Antisynch -ronization of uncertain unified chaotic systems with dead-zone nonlinearity, Nonlinear Analysis 68 (2008) 2629-2637, Physics Letters A 350 (2006) 36-43
[110]Rong-An Tang, Ya-Li Liu, Ju-Kui Xue, An extended active control for chaos synchronization, Physics Letters A 373 (2009) 1449-1454
[111]Tiegang Gao, Zengqiang Chen, Zhuzhi Yuan, Dongchuan Yu, Adaptive synchronization of a new hyperchaotic system with uncertain parameters, Chaos, Solitons and Fractals 33 (2007) 922-928
[112]Zheng-Ming Ge, Cheng-Hsiung Yang, Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control, Physica D 231 (2007) 87-94
[113]Wang-Long Li, Kuo-Ming Chang, Robust synchronization of drive-response chaotic systems via adaptive sliding mode control, Chaos, Solitons and Fractals,33, (2007) 280-284
[114]Pei Xinzhe, Liu Zhiyuan, Pei R.un, Robust trajectory tracking controller design for mobile robots with bounded input[J]. Acta automatica sinica,2003,29(6):876-881
[115]黄春庆,王兴贵,王祖光,输入力矩受限的机器人鲁棒自适应跟踪控制[J].控制理论与应用,2003,20(3)：338-343
[116]Ye Xudong. Adaptive nonlinear output-feedback control with unknown high frequency gain sign[J]. IEEE Trans on Automatic Control,2001,46(1):112-115
[117]Ge Shuzhi Sam, WANG J. Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients [J]. IEEE Trans on Automatic Control,2003,48(8): 1463-1469
[2]Hao B.L. Chaos II[M]. Singapore:World Scientific,1984
[3]Yong Wang, Kwok-Wo Wong, Xiaongfeng Liao, et al., A. new chaos-based fast image encryption algorithm[J]. Applied Soft Computing,2011(11):514-522
[4]Sivakumar B. Chaostheory in geophysics, past, present and future [J]. Chaos, Solitons & Fractals,2004,19(2):441-462
[5]关新平.混沌控制及其在保密通信中的应用[M].北京：国防工业出版社,2002.
[6]陈关荣,吕金虎Lorenz系统族的动力学分析、控制与同步[M].北京：科学出版社,2003,8.
[7]Poioncare.H科学的价值[M].北京：光明日报出版社,1988,356-38
[8]Lorenz EN. Deterministic non-periods flows. J Atmos Sci 1963;20:130-141.
[9]Ruelle D, Takens.F, On the nature of turbulence [J]. Comm.Math.Phys,1971,20:167-192.
[10]Li T Y and Yorke J A. Period three implies chaos[J]. Amer.Math.Monthly,1975,82:985-992.
[11]May R M. Simple mathematical models with very complicated dynamics[J]. Nature, 1976,261:459-463
[12]Feigenbaum M J.Quantitative universality for a class of nonlinear transformations[J]. J.Stat. Phys.,1978,19:25-52
[13]Mandelbort BB.The fractal geometry of nature[M],Califonia:W.Freeman Company,1980.
[14]Takens F. Deteming strange attractors in turbulence [J], Lecture notes in Math,1981,898: 361-381
[15]Grassberger P and Procaccia I. Measuring the strangeness of strange attractors[J]. Physica D, 1983,9:189-208
[16]Lv J.H, Chen G.R, A new chaotic attractor coined. Int J Bifurc Chaos 2002;12(3):659-61.
[17]Ott E, Grebogi C and Yorke J A. Controlling chaos[J], Phys.Rev.Lett.,1990,64:1196-1199.
[18]刘锋,穆肇骊,蔡远利等一类混沌系统的非线性反馈控制[J].控制与决策.2000,15(1)：15-18
[19]BemdaroM. An Adaptive approach to the control and synchronization of continuous time chaotic systems[J]. Int J Bifurcation and chaos.1996,6(3):557-568.
[20]GE S S, Wang C, Lee T H. Adaptive backstepping control of a class of chaotic systems[J]. Int J Bifurcation and chaos.2000,10 (5):1140-1156
[21]GE S S, Wang C, Adaptive control of uncertain Chua's circuits[J]. IEEE Trans Circuits System. 2000,47(9):1397-1402
[22]Alexander L, Fradkov, Markov A Yu. Adaptive synchronization of chaotic systems based on speed gradient method and passification[J]. IEEE Trans Circuits System 1997,44(10):905-912
[23]Dong X. Chen L. Adaptive control of the uncertain Duffing oscillator[J]. Int J Bifurcation and chaos.1997,7(7):1651-1658
[24]Tao Yang. Chun-Mei Yang and Lin-Bao Yang, A Detailed Study of Adaptive Contorl of Chaotic Systems with Unknown Parameters[J]. Dynamics and Control.1998,(8):255-267
[25]Oscar. Fuzzy control of chaos[J]. Int J Bifurcation and chaos.1998.8(8):1743-1747
[26]Liang Chen, Guanrong Chen, Lee Yang-Woo, Fuzzy modeling and adaptive control of uncertain chaotic systems[J]. Information Sciences.1999,121(1):27-37
[27]Liang Chen,Guanrong Chen.Fuzzy presictive control of uncertain chaotic Systems using time series[J].Int J Bifurcation and chaos.1999,9(40:757-767
[28]Chin Teng Lin.Controlling chaos by GA-based reinforcement learning neural network[J]. IEEE Trans On neural networks.1999,10:846-859
[29]王忠勇,蔡远利,贾冬等.混沌系统的神经网络控制[J].控制与决策.2000,15(1)：55-58
[30]Nussbaum, R. D. (1983). Some remarks on the conjecture in parameter adaptive control[J]. Systems and Control Letters,3(3),243-246
[31]MARTENSSON B. Remarks on adaptive stabilization of first order nonlinear systems[J]. Systems & Control Letters,1990,14(1):1-7
[32]RYAN E P. A universal adaptive stabilizer for a class of nonlinear systems[J]. Systems & Control Letters,1991,16(3):209-218.
[33]RYAN E P. A nonlinear universal servomechanism[J]. IEEE Trans on Automatic Control, 1994,39(4):753-761.
[34]DING Z. Adaptive control of nonlinear systems with unknown virtual control coefficients[J]. Int J of Control Signal Processing,2000,14(4):505-517.
[35]YE X, JIANG J. Adaptive nonlinear design without a priori knowledge of control directions [J]. IEEE Trans on Automatic Control,1998,43(11):1617-1621.
[36]GE Shuzhi Sam, WANG J. Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems[J]. IEEE Trans on Neural Networks,2002,13(11):1409-1419.
[37]YE X D. Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control directions[J]. Automatica,1999,35(5):929-935.
[38]Ye, X. D.,& Jiang, J. P. (1998). Adaptive nonlinear design without a prioriknowledge of control directions. IEEE Transactions on Automatic Control,43(11),1617-1621.
[39]Ge, S. S., Hong, F.,& Lee, T. H. (2004). Adaptive neural control of nonlinear time-delay system with unknown virtual control coefficients.IEEE Transactions on Systems, Man, and Cybernetics-PartB:Cybernetics,34(1),499-516.
[40]Yan Li, YangQuan Chen, When is a Mittag-Leffler function a Nussbaum function? Automatica 45 (2009) 1957-1959
[41]T.P.Zhang, S.S.Ge Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs, Automatica 43(2007) 1021-1033
[42]Yang C, Ge SS, Xiang C, Chai TY, Lee TH. Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Transactions on Neural Networks 2008; 19(11):1873-86.
[43]Weisheng Chen, Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints, ISA Transactions 48 (2009) 304-311
[44]Jagannathan S, He P. Neural-network-based state-feedback control of a nonlinear discrete-time system in nonstrict feedback form. IEEE Transactions on Neural Networks 2008;19(12):2073-2087
[45]魏春玲,王强德,武玉强,控制方向未知的高次非线性系统的鲁棒自适应控制[J].控制理论与应用,Vol.24 No.4,2007,519-525
[46]Pecora.L.M. and Carroll.T.L. Synchronization of chaotic systems. Phys.Rev. Lett, 1990A(64):821-832
[47]凌复华.混沌,随机,信息流和其它[J].力学与实践.1985,7(5)：17-20
[48]T.Kapitaniak et al. Experimental synchronization of chaos using continous control. Int.J. Bifurcation and Chaos,1999,4(2):483-488
[49]R.Roy et al. Experimental synchronization in laser chaos. Phys. Rev. Lett,1994,72(22): 3502-3505
[50]T.Sugawara, Ttachikawa. Observation of synchronization in laser chaos. Phys.Rev.Lett, 1994,72(22):3502-350
[51]Gao Ping Jing et al. A simple global synchronization criterion for coupled chaotic systems. Solitons and fractals.2003,(15):925-935
[52]Jianping Yan, Changpin Li. On synchronization of three chaotic systems. Chaos,Solitons and fracrals.2005,(23):1683-1688
[53]C.Sarasola,F.J.Torrealdea,A.D Anjou. Feedback synchronization of chaotic Systems[J]. Int.J. Bifurcation and chaos.2003,13(1):177-191
[54]M.T.Yassen.Chaos synchronization between two different chaotc systems using active control.Chaos,Solitons & Fractals.2005:23(4):131-140
[55]H.N.Agiza,M.T.Yassen. Synchronization of Rossler and Chen chaotic dynamical systems using active control.Physics Letters A.2001,(278):191-197
[56]Ming-chung Ho, Yao-Chen Hung.Synchronization of two different systems by Using generalized active control. Physics Letters A.2002,(301):424-428.
[57]Jiang G.P., Tang K.S. A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach. Int. J. Bifurcation Chaos,2002,12(10):2239-2253
[58]Bu S.L., Wang S.Q.An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems. Physica D,2002,164:45-52
[59]高金峰,罗先觉,马西奎.控制与同步连续时间混沌系统的非线性反馈方法[J].物理学报,1999,48(9)：1618-1627
[60]刘杨正,费树岷Genesio-Tesi和Coullet混沌系统之间的非线性反馈同步[J].物理学报,2005,54(8)：3486-3490
[61]陶朝海,陆景安.混沌系统的速度反馈同步[J].物理学报,2005,54(11)：5058-5061
[62]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[J].控制与决策,2001,16(4)：476-479
[63]张宇,余俊明,杜功焕.连续反馈混沌同步方式在保密通讯中的应用[J].科学同步,1998,43(17)：1831-1835
[64]Kouomou Y.C., Woafo P. Stability and optimization of Chaos synchronization through feedback coupling with delay [J]. Physics Letters A,2002,298:18-28
[65]Suykens. J.A.K, Robust nonlinear H∞ synchronization of chaotic Lur's system, IEEE Trans Circuit & System1997,44(10):891-903
[66]Michele B, Donato C. Synchronization of hyper-chaotic circuits via continuous feedback control with application to secure communication. Int. J. Bifurcation and Chaos, 1998,8(10):2031-2040
[67]Alexander L.Fradkov, A Yu.Markov. Adaptive synchronization of chaotic system phased on speed gradient method and passification. IEEE Trans on Circuit Syst.(Ⅰ),1997,44(10):905-912
[68]Young_Hoon Joo, Leang-San shieh, Guangrong Chen, Hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems, IEEE Trans on Fuzzy Syst.(Ⅰ),1999,7(4):394-408
[69]Alexander Pogromsky, Henk Nijmeijer. Observer-based robust synchronization of dynamical systems. Int,J. Bifurcation and Chaos,1998,8(11):2243-2254
[70]E.M.Elabbasy,H.N.Agiza,M.M.El-dessoky.Adaptive synchronization of lv System with uncertain parameters. Chaos,solitons and fractals.2004,(21):657-667
[71]M.T.yassen. Adaptive synchronization of Rosser and lu systems with fully uncertain patameters. Chaos,solitons and fractals.2005,(23):1527-1536
[72]Ju H.Park. Adaptive sysnchronization of Rossler system with uncertain Parameters.Chaos, solitons and fractals.2005,(22):1-6
[73]T.L. Liao.Adaptive synchronization of two Lorenz system. Chaos.solitons and fractals.1998, 9(9):1555-1561
[74]Yongguang Yu, Suochun Zhang, Adaptive backstepping synchronization of uncertain chaotic system[J]. Chaos, Solitons and Fractals 21 (2004) 643-649
[75]M.T. Yassen, Adaptive chaos control and synchronization for uncertain new chaotic dynamical system[J], Physics Letters A 350 (2006) 36-43
[76]Awad El Gohary, Rizk Yassen, Adaptive control and synchronization of a coupled dynamic system with uncertain parameters[J], Chaos, Solitons and Fractals 29 (2006) 1085-1094
[77]Qiang Jia, Adaptive control and synchronization of a new hyperchaotic system with unknown parameters [J], Physics Letters A 362 (2007) 424-429
[78]Rongwei Guo, A simple adaptive controller for chaos and hyperchaos synchronization, Physics Letters A,360 (2009) 38-53
[79]Wei Lin, Adaptive chaos control and synchronization in only locally Lipschitz systems, Physics Letters A 372 (2008) 3195-3200
[80]Jian Huang, Adaptive synchronization between different hyperchaotic systems with fully uncertain parameters, Physics Letters A 372 (2008) 4799-4804
[81]Ju H. Park, S.M. Lee, O.M. Kwon, Adaptive synchronization of Genesio-Tesi chaotic system via a novel feedback control, Physics Letters A 371 (2007) 263-270
[82]Xianyong Wu, ZhiHong Guan, Zhengping Wu, Adaptive synchronization between two different hyperchaotic systems, Nonlinear Analysis 68 (2008) 1346-1351
[83]Ming-Chung Ho, Yao-Chen Hung, Zhi-Yu Liua, I-Min Jiang, Reduced-order synchronization of chaotic systems with parameters unknown, Physics Letters A 348 (2006) 251-259
[84]Jui-Sheng Lin, Jun-Juh Yan, Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller, Nonlinear Analysis:Real World Applications,68 (2008) 1346-1351
[85]Tsung-Ying Chiang, Jui-Sheng Lin,Teh-Lu Liao, Jun-Juh Yan, Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity, Nonlinear Analysis 68 (2008) 2629-2637
[86]Her-Terng Yau, Jun-Juh Yan, Chaos synchronization of different chaotic systems subjected to input nonlinearity, Applied Mathematics and Computation 197 (2008) 775-788
[87]李聪颖,牟丽君,考虑控制受限的AWCT增益调度及其在飞航导弹控制系统中的应用,第二届机电一体化与智能材料国际会议,中国桂林,2012
[88]黄显林,葛东明,输入受限高超声速飞行器鲁棒变增益控制,第二届机电一体化与智能材料国际会议(系统工程与电子技术期刊),中国桂林,2012
[89]Wanli Guo, Shihua Chen, Hong Zhou, A simple adaptive-feedback controller for chaos synchronization, Chaos, Solitons and Fractals 39 (2009) 316-321
[90]Guoyuan Qi, Zengqiang Chen, Zhuzhi Yuan, Adaptive high order differential feedback control for affine nonlinear system, Chaos, Solitons and Fractals 37 (2008) 308-315
[91]Yan-Wu Wang, Changyun Wen, Yeng Chai Soh, Jiang-Wen Xiao, Adaptive control and synchronization for a class of nonlinear chaotic systems using partial system states, Physics Letters A 351 (2006)79-84
[92]邱道尹,张健.基于单神经元的自适应PID控制系统设计及仿真[J].华北水利水电学院学报,2011(1)：34-36
[93]徐峰,李东海,适应型PID控制器参数整定性能比较[J].电子技术应用,2002(6)：135-137
[94]赵建华,沈永良,一种自适应PID控制算法[J].自动化学报,2001,27(3)：417-420
[95]李亮,康铭鑫,汽车牵引力控制系统的变参数自适应PID控制[J].机械工程学报,2011,47(12)：217-224
[96]侯砚泽,董朝阳,王青,邓舞燕,不确定切换系统的鲁棒自适应控制方案[J].北京航空航天大学学报,Vol.35 Issue (4):444-448
[97]柯海森,叶旭东,钱建海,移动机器人的鲁棒自适应控制器设计[J].浙江大学学报,2006,40(7)：1127-1131
[98］关新平,唐英干,基于神经网络的混沌系统鲁棒自适应同步[J].物理学报,2001,50(11)：1127-1131
[99]王宏伟.于双和,基于Chebyshev正交神经网络的混沌系统鲁棒自适应同步[J].控制理论与应用,2009,26(10)：1100-1105
[100]方敏,王经维,一种增益可调的极点配置自校正调节器的显式和隐式算法[J].控制理论与应用,1991,8(4)：401-406
[101]单剑锋,杨立军,极点配置自校正PID调节器[J].抚顺石油学院学报,2002(1)：12-13
[102]Alban Puai Man Tsui,Antonia J. Jones, Periodic response to external stimulation of a chaotic neural network with delayed feedback[J]. International journal of bifurcation and chaos in applied sciences and engineering,1999,9(4):322-329
[103]程丽,彭建华,极点配置法确定超混沌系统同步与控制的条件[J].广西师范大学学报,2002(1)：34-36
[104]Haitao Yu, Jiang Wang, Bin Deng, Adaptive backstepping sliding mode control for chaos synchronization of two coupled neurons in the external electrical stimulation [J]. Commun Nonlinear Sci Numer Simulat 17 (2012) 1344-1354
[105]Chao-Lin Kuo, Design of a fuzzy sliding-mode synchronization controller for two different chaos systems, Computers and Mathematics with Applications 61 (2011) 2090-2095
[106]Her-Terng Yau, Design of adaptive sliding mode controller for chaos synchronization with uncertainties, Chaos, Solitons and Fractals 22 (2004) 341-347
[107]Her-Terng Yau, Jun-Juh Yan, Chaos synchronization of different chaotic systems subjected to input nonlinearity, Applied Mathematics and Computation 197 (2008) 775-788
[108]Jui-Sheng Lin, Jun-Juh Yan,, Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller, Nonlinear Analysis:Real World Applications,68 (2008) 1346-1351
[109]Tsung-Ying Chiang, Jui-Sheng Lin Teh-Lu Liao, Jun-Juh Yan, Antisynch -ronization of uncertain unified chaotic systems with dead-zone nonlinearity, Nonlinear Analysis 68 (2008) 2629-2637, Physics Letters A 350 (2006) 36-43
[110]Rong-An Tang, Ya-Li Liu, Ju-Kui Xue, An extended active control for chaos synchronization, Physics Letters A 373 (2009) 1449-1454
[111]Tiegang Gao, Zengqiang Chen, Zhuzhi Yuan, Dongchuan Yu, Adaptive synchronization of a new hyperchaotic system with uncertain parameters, Chaos, Solitons and Fractals 33 (2007) 922-928
[112]Zheng-Ming Ge, Cheng-Hsiung Yang, Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control, Physica D 231 (2007) 87-94
[113]Wang-Long Li, Kuo-Ming Chang, Robust synchronization of drive-response chaotic systems via adaptive sliding mode control, Chaos, Solitons and Fractals,33, (2007) 280-284
[114]Pei Xinzhe, Liu Zhiyuan, Pei R.un, Robust trajectory tracking controller design for mobile robots with bounded input[J]. Acta automatica sinica,2003,29(6):876-881
[115]黄春庆,王兴贵,王祖光,输入力矩受限的机器人鲁棒自适应跟踪控制[J].控制理论与应用,2003,20(3)：338-343
[116]Ye Xudong. Adaptive nonlinear output-feedback control with unknown high frequency gain sign[J]. IEEE Trans on Automatic Control,2001,46(1):112-115
[117]Ge Shuzhi Sam, WANG J. Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients [J]. IEEE Trans on Automatic Control,2003,48(8): 1463-1469