几类混沌系统的控制与应用研究
|
摘要
对混沌现象的研究是非线性科学中重要课题之一，混沌运动是一种确定性的类随机运动，它广泛存在于客观世界中，由于混沌的奇异特性，不施加控制的混沌将无法应用，混沌控制是混沌走向应用的第一步，因此混沌系统控制与应用的研究成为非线性科学的研究热点。
本课题沿着混沌控制(狭义)和混沌同步为主线在国家自然科学基金“时滞混沌系统的控制和同步研究” 和河北省自然科学基金“混沌保密通信技术及应用研究”的资助下主要研究了以下几方面的内容：
(1)运用Backstepping方法对含有不确定性的严格反馈混沌系统进行控制，分别基于连续函数补偿和RBF神经网络补偿取得了较好的控制效果。基于特殊的滑模控制方法结合参数辨识对含有未知参数的统一混沌系统实现了不稳定不动点的跟踪控制。
(2)研究了扰动情况下混沌系统的恒等同步与线性广义同步问题，首先利用线性变换对混沌系统进行扰动解耦，使得受扰动部分可用未受扰部分和系统输出来表示，然后利用两种非线性观测器重构混沌系统实现恒等同步。同时借鉴线性系统中含有未知输入的观测器设计方法，将扰动看作是未知输入实现了时滞混沌系统的线性广义同步。
(3)首次提出了弹性同步的概念。考虑到不只混沌系统自身会受到扰动或不确定性的影响，而且控制器在很多情况下也不能精确实现，存在一定程度的摄动，其对同步产生的影响有时是巨大的，为此在摄动界已知和未知两种情况下分别给出了弹性同步控制器的增益形式。
(4)研究了混沌在保密通信领域的应用问题，基于VC++编写了加密软件实现对图像文件的加密，软件采用混沌遮掩与混沌置乱两级加密原则，具有执行速度快，加密程度高等优点。
Research on chaos is one of the important achievements in nonlinear science. Chaotic motion is a complex motion, whose equation is certain but the trajectory of the orbits is stochastic. There are lots of chaotic phenomena in real world. For oddities of chaos, uncontrolled chaos will not be applied, so chaos control is the first step of chaos application. Chaos control and cha0os application have already become hot field in nonlinear science.
This project is supported by National Science Foundation of China and Hebei Science Foundation. Along the chaos control(narrow sense) and chaos synchronization, the main results of this thesis are expressed as follows:
(1)By backstepping method, the strict-feedback chaotic system with uncertainties was stabilized, in which we applied continuous function and RBF neural network to compensate the uncertainties. The control aim was realized. Based on special sliding-mode control with parameter identification, the unified chaos was led to unstable equilibrium point.
(2)Chaos identical synchronization and linear generalized synchronization was studied. Firstly we divided the chaos with perturbation into two parts, furthermore denoted the perturbed part by unperturbed part and output. Secondly by two nonlinear observers we realized the chaos identical synchronization. At the same time, according to unknown input linear observer, the linear generalized synchronization controller was designed.
(3)For the first time, the resilient synchronization was put forward. The uncertainties or perturbation not only exist in chaos itself but also in controller, namely the controller can’t be implemented exactly, which may be deadly to synchronization. To solve the problem, we design the resilient controller under known and unknown disturbed bound.
(4)Chaos application in secure communication was introduced. Based
on VC++, we developed image encryption software, in which chaos masking and chaos image permutation was adopted. Simulation results showed that the software implemented quickly and encrypted highly.
本课题沿着混沌控制(狭义)和混沌同步为主线在国家自然科学基金“时滞混沌系统的控制和同步研究” 和河北省自然科学基金“混沌保密通信技术及应用研究”的资助下主要研究了以下几方面的内容：
(1)运用Backstepping方法对含有不确定性的严格反馈混沌系统进行控制，分别基于连续函数补偿和RBF神经网络补偿取得了较好的控制效果。基于特殊的滑模控制方法结合参数辨识对含有未知参数的统一混沌系统实现了不稳定不动点的跟踪控制。
(2)研究了扰动情况下混沌系统的恒等同步与线性广义同步问题，首先利用线性变换对混沌系统进行扰动解耦，使得受扰动部分可用未受扰部分和系统输出来表示，然后利用两种非线性观测器重构混沌系统实现恒等同步。同时借鉴线性系统中含有未知输入的观测器设计方法，将扰动看作是未知输入实现了时滞混沌系统的线性广义同步。
(3)首次提出了弹性同步的概念。考虑到不只混沌系统自身会受到扰动或不确定性的影响，而且控制器在很多情况下也不能精确实现，存在一定程度的摄动，其对同步产生的影响有时是巨大的，为此在摄动界已知和未知两种情况下分别给出了弹性同步控制器的增益形式。
(4)研究了混沌在保密通信领域的应用问题，基于VC++编写了加密软件实现对图像文件的加密，软件采用混沌遮掩与混沌置乱两级加密原则，具有执行速度快，加密程度高等优点。
Research on chaos is one of the important achievements in nonlinear science. Chaotic motion is a complex motion, whose equation is certain but the trajectory of the orbits is stochastic. There are lots of chaotic phenomena in real world. For oddities of chaos, uncontrolled chaos will not be applied, so chaos control is the first step of chaos application. Chaos control and cha0os application have already become hot field in nonlinear science.
This project is supported by National Science Foundation of China and Hebei Science Foundation. Along the chaos control(narrow sense) and chaos synchronization, the main results of this thesis are expressed as follows:
(1)By backstepping method, the strict-feedback chaotic system with uncertainties was stabilized, in which we applied continuous function and RBF neural network to compensate the uncertainties. The control aim was realized. Based on special sliding-mode control with parameter identification, the unified chaos was led to unstable equilibrium point.
(2)Chaos identical synchronization and linear generalized synchronization was studied. Firstly we divided the chaos with perturbation into two parts, furthermore denoted the perturbed part by unperturbed part and output. Secondly by two nonlinear observers we realized the chaos identical synchronization. At the same time, according to unknown input linear observer, the linear generalized synchronization controller was designed.
(3)For the first time, the resilient synchronization was put forward. The uncertainties or perturbation not only exist in chaos itself but also in controller, namely the controller can’t be implemented exactly, which may be deadly to synchronization. To solve the problem, we design the resilient controller under known and unknown disturbed bound.
(4)Chaos application in secure communication was introduced. Based
on VC++, we developed image encryption software, in which chaos masking and chaos image permutation was adopted. Simulation results showed that the software implemented quickly and encrypted highly.
引文
G. Chen, X. Wang. Identification and Control of Chaotic Systems: Artificial Neural Network Approach. Proc. of IEEE Int. Symp. on Circ. System, 1995,42(11):1177-1182
T. L. Carroll. Synchronization and Complex Dynamics in Pulse-coupled Circuit Models of Neurons. Biol. Cyber., 1995,(73):553-559
张辉,吴淇泰.受迫Duffing振子中的混沌控制.非线性动力学学报, 1995,(2):356-360
K. Murali, M. Lakshmanan. Transmission of Signal by Synchronization in a Chaotic Van der Pol-Duffing Oscillator. Phys. Review E, 1993,48(3):1624-1626
A. V. Namenko, N. A. Loiko. Chaos Control in External Cavity Laser Diodes Using Electronic Impulsive Delayed Feedback. Int. J. Bif. and Chaos, 1998,8(9):1791-1799
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论文].2001:1-2
吴祥兴,陈忠.混沌学导论.上海:上海科技文献出版社,1996:120-143
黄润生.混沌及其应用.武汉:武汉大学出版社,2000:125-145
L. D. Iasemidis, J. C. Sackellares Phase Space Topography and the Lyapunov Exponent of Ectrocorticograms in Partial Seizures. Brain Topogr, 1990,(2):187-201
E. Ott, C. Grebogi, and J. A. York. Controlling Chaos. Phys. Rev. Lett. A, 1990, (64):1196-1199
W. D. Ditto, S. N. Rauseo, and M. Spano. Experimental Control of Chaos. Phys. Rev. Lett. A, 1990,(65):3211-3214
方锦清.非线性系统中混沌的控制与同步及其应用前景(一).物理学进展,1996, 16(1):1-23
K. Pyragas. Continuous Control of Chaos by Self-controlling Feedback. Phys. Lett. A, 1992,(170):421-428
K. Pyragas. Experimental Control of Chaos by Delayed Self-controlling Feedback. Phys. Lett. A, 1993,(180):99-102
G. Chen，X.Yu. On Time-delayed Feedback Control of Chaotic Systems. IEEE Trans. on CAS., 1999,46(6):767-772
X. Guan, C. Chen, and H. Peng. Time-Delayed Feedback Control of Time-delay Chaotic Systems. Int. J. Bif. and Chaos, 2003,13(1):193-205
B. A. Huberman. Dynamics of Adaptive Systems. IEEE Trans. on CAS., 1990, 37(4):547-550
D. Vassiliadis. Parametric Adaptive Control and Parameter Identification of Low Dimensional. Chaotic Systems. Physica D, 1994,(71):319-341
Y. Tian. Adaptive Stabilization of Unstable Periodic Orbits of Chaotic Systems. Proceedings of the 3rd World Congress on Intelligent Control and Automation, Hefei, P.R.China, 2000:3195-3199
P. M. Alsing, A. Garielides. Using Neural Networks for Controlling Chaos. Phys. Rev. E, 1994,(49):1225-1231
C. T. Lin. Controlling Chaos by GA-based Reinforcement Learning Neural Network. IEEE Trans. on Neural Networks, 1999,(10):846-859
L. Chen, G. Chen Fuzzy Predictive Control of Uncertain Chaotic Systems Using Time Series. Int. J. Bif. and Chaos, 1999,9(4):757-767
X. Liu. Impulsive Control of Chaotic System. Int. J. Bif. and Chaos, 2002,12 (5):1181-1190
J. Sun, Y. Zhang. Impulsive Control of Systems. Phys. Lett. A, 2003, (306):306-312
B. R. N. Nbendjo, R. Tchoukuegno and P.Woafo. Active Control with Delay of Vibration and Chaos in a Double-well Duffing Oscillator. Chaos, Solitons and Fractals, 2003,18(2):773-792
S. Yang, C.Chen and H.Yau. Control of Chaos in Lorenz System. Chaos, Solitons and Fractals, 2002,13(4):773-792
H. Yau, C. Chen and C. Chen. Sliding Mode Control of Chaotic Systems with Uncertainties. Int. J. Bif. and Chaos, 2000,10(5):1139-1147
S. S. Ge, C. Wang and T. H. Lee. Adaptive Backstepping Control of a Class of Chaotic Systems. Int. J. Bif. and Chaos, 2000,10(5):1149-1156
T. Wu, Min-S. Chen. Chaos Control of the Modified Chua’s Circuit System. Physica D, 2002,164:53-58
L. M. Pecora, T. L. Carroll. Synchronization of Chaotic Systems. Phys. Rev. Lett. A,1990, (64):821-832
方锦清.非线性系统中混沌的控制与同步及其应用前景(二).物理学进展,1996, 16(2):137-196
J. A. K. Suykens, P. F. Curran. Robust Nonlinear Synchronization of Chaotic Lur’e System. IEEE Trans.on CAS., 1997,44(10):2031-2040
B. Michele, C. Donato. Synchronization of Hyper-chaotic Circuits via Continuous
Feedback Control with Application to Secure Communication. Int. J. Bif. and Chaos, 1998,8(10):2031-2040
C. Cruz, Synchronization through Filtering. Int. J. Bif. and Chaos, 2000, 10 (5):763-775
F. Liu., Y. Ren and X. Shan, et al. A Linear Feedback SynchronIzati on Theorem for a Class of Chaotic Systems. Chaos, Solitons and Fractals, 2002,13(4):723-730.
Y. Hong, H. Qin. Adaptive Synchronization of Chaotic systems via Output Feedback Control. Int. J. Bif. and Chaos, 2001,11(8):1149-1158
Y. Joo, L. Shieh and G. 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
H. Nijmeijer. A Dynamical Control View on Synchronization, Physica. D, 2001, (154):219-228
关新平,范正平,彭海朋.对一类具有随机扰动的混沌系统同步的新方法.电子学报, 2001,29(10):211-215
L. Kanellakopulos, P. V. Kokotovic and A. S. Morse. Systernatic Design of Adaptive Controllers for Feedback Linearizable Systems. IEEE Trans. on Automatic Control, 1991, 36(11):1241-1253
J. L, S. Zhang. Controlling Chen’s Chaotic Attractor Using Backstepping Design Based on Parameters Identification. Phys. Lett. A, 2001,(286):148-152
C. Wang, S. S. Ge. Adaptive Backstepping Control of Uncertain Lorenz System. Int. J. Bif. and Chaos, 2001,11(4):1115-1119
范正平,唐应干,关新平.一类混沌系统的鲁棒自适应控制研究.第14届控制与决策年会论文集.西安, 2001:50-53
S. S. Ge, C. Wang. Uncertain Chaotic System Control via Adaptive Neural Design. Int. J. Bif. and Chaos, 2002,12(5):1097-1109
宫琪,田玉平.非线性交叉严格反馈系统的一种构造性设计方法.自动化学报,2000, 26(4):447-453
王强德,陈卫田,魏春玲,等.一类不确定非线性系统的鲁棒自适应控制.控制理论与应用,2000,17(2):244-248
吴锋民,江春叶.Duffing方程的准混沌现象.浙江大学学报(自然科学版),1994, 21(3):339-340
刘宗华,方海平.Areneodo模型的研究.广西大学学报,1994,19(4):321-326
R. M. Sanner, J. E. Slotine. Gaussian Networks for Direct Adaptive Control. IEEE Trans. on Neural Networks, 1992,3(6):837-863
S. Chen, J. L. Synchronization of an Uncertain Unified Chaotic System via Adaptive Control. Chaos, Solitons and Fractals, 2002,14(3):643-647
G. Chen, U. Ueta. Yet Another Chaotic Attractor. Int. J. Bif. and Chaos, 1999, 9(7):1465-1466
关新平,彭海朋,李丽香等.Lorenz混沌系统的参数辨识与控制.物理学报,2001, 50(1):26-29
邹恩,李祥飞,陈建国.混沌控制及其优化应用.长沙:国防科技大学出版社,2002:32-33
方锦清.驾驭混沌与发展高新技术.北京:原子能出版社,2002:125, 239-248
L. Kocarev, U. Parisi. Generalized Synchronization, Predictability, and Equivalence of Unidirectionally Coupled Dynamical Systems. Phys. Rev. Lett.,1996,(76):1816-1819
J. Lu, Y. Xi. Linear Generalized Synchronization of Continuous-time Chaotic Systems. Chaos, Solitons and Fractals, 2003,17(5):825-831
郑大钟.线性系统理论.北京:清华大学出版社,1990:197
H. Nijmeijer, I. Mareels. An Observer Looks at Synchronization. IEEE Trans. on CAS., 1997,44(10):882-890
杨晓松.一类混沌系统观测器.物理学报,2000,49(10):1919-1203
U. Toshimitsu, Synthesis of Synchronized Chaotic Systems Based on Observers, Int. J. Bif. and Chaos, 1998,9(3):541-546
蒋国平,王锁平.基于状态观测器的超混沌系统同步方法研究,电子学报,2000, 28(1):108-110.
X. F. Wang, Z. Q. Wang, Synchronizing Chaos and Hyperchaos with Any Scalar Transmitted Signal, IEEE Trans. on CAS.,1998,45(10):1101-1103
马克茂,王子才,史小平.一类非线性系统的观测器设计.控制理论与应用,1998, 15(3):443-446
G. R. Duan. Solutions to Matrix Equation and Their Application to Eigen Structure Assignment in Linear Systems. IEEE Trans. on Automatic Control, 1993, 38(2):276-280
T. Matsumoto L. O. Chua and K. Kobayashi, et.al. Hyperchaos: Laboratory Experiment and Numerical Confirmation. IEEE Trans. on CAS., 1986,33(11):1143-1147
D. Koenig, S. Mammar. Design of a Class of Reduced Order Unknown Inputs Nonlinear Observer or Fault Diagnosis. Proceedings of the American Control Conference, Arlington,
VA, 2001:2143-2147
S. Magdi, Mahmoud. Robust control of Discrete Systems with Uncertain Parameters and Unknown Delays. Automatica, 2000,36(4): 627-635
T. Ushio, T. Innami S. Kodama. Chaos Shift Keying Based on In-phase and Anti-phase Chaotic Synchronization, IEICE Trans. Fundamental E79-A 10:1689-1693
G. Perez, H. A. Cerderra. Extracting Message Masked by Chaos. Phys. Rev. Lett. 1995, (74):1970-1973
M. K. Ali, J. Fang. Synchronization of Chaos and Hyperchaos Using Linear and Nonlinear Feedback Functions. Phys Rev E, 1997,(55):5285-5290
A. Namajunas. Analog Techniques for Modeling and Controlling the Mackey-Glass System. Int. J. Bif. and Chaos, 1998,8(7):957-962
F. Yang, R. W. Wilde. Observers for Linear Systems with Unknown Inputs. IEEE Trans. on Automatic. Control, 1988,33(6):677-681
L. H. Keel, S. P. Bhattacharyya. Robust Fragile or Optimal? IEEE Trans. on Automatic. Control, 1997,42(8):1098-1105
G. H. Yang, J. L. Wang and Y. C. Soh. Guaranteed Cost Control for Discrete-Time Linear Systems under Controller Gain Perturbations. Linear Algebra and its Applications, 2000, (312):161-180
D. Famularo, P. Dorato and C. T. Abdallah, et.al. Robust Non-Fragile LQ Controllers: the Static State Feedback Case, Int. J. Control, 2000,73(2): 159-165
邬晶.时滞系统的鲁棒稳定性分析与弹性控制器设计.[燕山大学硕士学位论文]. 2002:63-72
L. H. Keel S. P. Bhattacharyya. Author’s Reply. IEEE Trans. on Automatic Control. 1998, 43(9):1268
L. O. Chua. Chua’s Circuit-an Overview Ten Years Later. J Circuit Sys. Computer, 1994, (4):117-159
R. N. Madan. Chua’s Circuit:a Paradigm for Chaos. Singapore: World Scientific, 1993:34
K. Neal. A Course in Number and Theory and Cryptography. Spring-Verlag, 世界图书出版公司,1990:68
沈世镒,近代密码学.桂林:广西师范大学出版社,1999:78
W. Bender, D. Gruhl, and N. Morimoto. et.al.Techniques for Data Hiding. IBM System Journal, 1996,35(3):313-335
禹思敏,丘水生,罗伟民.混沌通信的研究进展与综合评述.桂林电子工业学院学报,
2000, 20(1):56-62
H. Fujisaka, T. Yamada. Stability Theory of Synchronized Motion in Coupled-oscillator Systems. Pro. Theo. Phys., 1983,(69):32-47
K.M. Cuomo, A. V. Oppenheim. Circuit Implementation of Synchronized Chaos with Application to Communications. Phys. Rev. Lett., 1993,(71):65-68
胡岗,萧井华,郑志刚.混沌控制.上海:上海科技教育出版社,2000:171-175
P. Yu, T. Lookman. Exact Recovery from Masked Chaotic Signal. Mini Symposium Cryptograghy, Toronto:Canadian Applied Mathematics Society, 1997:18-25
匡锦瑜,裴留庆.一种多级混沌同步通信系统.电子学报,1999,27(6):23-26
李建芬,李农.一种新的蔡氏混沌掩盖通信方法.系统工程与电子技术,2002,24(4):41-43
易开祥,孙鑫,石教英.一种基于混沌序列的图像加密算法.计算机辅助设计与图形学学报,2000,12(9):672-676
李昌刚,韩正之,张浩然.一种基于指数性混沌序列的灰度图像加密算法.计算机工程与应用,2001,(8):16-25
陆卫兵,彭建华,乔双.超混沌网络保密通讯软件的研究.东北师大学报(自然科学版), 2001,33(2):111-114
郝柏林.从抛物线谈起—混沌动力学引论.上海:上海科技教育出版社,1993:35
王光瑞,陈光旨.非线性常微分方程的混沌运动.南宁:广西科学技术出版社,1995:48
赵耿,郑德玲,方锦清.混沌保密通信的最新进展.自然杂志,23(2):97-107
攻读硕士学位期间参加的科研课题
“时滞混沌系统的控制和同步研究”,国家自然科学基金,( No:60274023)
“混沌保密通信技术及应用研究”,河北省自然科学基金,( No: 601225)
攻读硕士学位期间的科学研究成果
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
关新平,何宴辉，范正平等.一类参数未知混沌系统的鲁棒自适应控制.控制与决策, 2003,18(3):324-327
关新平,何宴辉,邬晶.基于弹性控制器的混沌同步.物理学报, 2003,52(11): 2718-2722
关新平,何宴辉,唐英干.随机扰动下一类混沌系统的同步.系统工程与电子技术(待发表)
何宴辉,范正平,关新平.一类混沌系统基于观测器的鲁棒同步控制.第14届控制与决策年会论文集,西安, 2002:65-69
关新平,何宴辉.扰动下连续时滞混沌系统的线性广义同步.中国矿大博士后讲坛
Guan Xinping, He Yanhui. Stabilizing UEP of Unified Chaotic System with Unknown Parameter Using Sliding Mode Control. Chinese Physics Letters. 2004,21(2):227-229
He Yanhui, Chen Cailian, Liu Tongshuan, Guan Xinping. Adaptive Backstepping Control of a Chaotic System Using RBF Neural Networks. IEEE Intelligent Automation Conference, Hong Kong, 2003:68-71
关新平,彭海朋,何宴辉.具有随机扰动连续时滞混沌系统的同步.系统工程与电子技术, 2002, 24(9):74-77
关新平,范正平,何宴辉.混沌控制综述.燕山大学学报(中国自动化学会,2001,北戴河学术年会专刊), 25:1-4
T. L. Carroll. Synchronization and Complex Dynamics in Pulse-coupled Circuit Models of Neurons. Biol. Cyber., 1995,(73):553-559
张辉,吴淇泰.受迫Duffing振子中的混沌控制.非线性动力学学报, 1995,(2):356-360
K. Murali, M. Lakshmanan. Transmission of Signal by Synchronization in a Chaotic Van der Pol-Duffing Oscillator. Phys. Review E, 1993,48(3):1624-1626
A. V. Namenko, N. A. Loiko. Chaos Control in External Cavity Laser Diodes Using Electronic Impulsive Delayed Feedback. Int. J. Bif. and Chaos, 1998,8(9):1791-1799
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论文].2001:1-2
吴祥兴,陈忠.混沌学导论.上海:上海科技文献出版社,1996:120-143
黄润生.混沌及其应用.武汉:武汉大学出版社,2000:125-145
L. D. Iasemidis, J. C. Sackellares Phase Space Topography and the Lyapunov Exponent of Ectrocorticograms in Partial Seizures. Brain Topogr, 1990,(2):187-201
E. Ott, C. Grebogi, and J. A. York. Controlling Chaos. Phys. Rev. Lett. A, 1990, (64):1196-1199
W. D. Ditto, S. N. Rauseo, and M. Spano. Experimental Control of Chaos. Phys. Rev. Lett. A, 1990,(65):3211-3214
方锦清.非线性系统中混沌的控制与同步及其应用前景(一).物理学进展,1996, 16(1):1-23
K. Pyragas. Continuous Control of Chaos by Self-controlling Feedback. Phys. Lett. A, 1992,(170):421-428
K. Pyragas. Experimental Control of Chaos by Delayed Self-controlling Feedback. Phys. Lett. A, 1993,(180):99-102
G. Chen，X.Yu. On Time-delayed Feedback Control of Chaotic Systems. IEEE Trans. on CAS., 1999,46(6):767-772
X. Guan, C. Chen, and H. Peng. Time-Delayed Feedback Control of Time-delay Chaotic Systems. Int. J. Bif. and Chaos, 2003,13(1):193-205
B. A. Huberman. Dynamics of Adaptive Systems. IEEE Trans. on CAS., 1990, 37(4):547-550
D. Vassiliadis. Parametric Adaptive Control and Parameter Identification of Low Dimensional. Chaotic Systems. Physica D, 1994,(71):319-341
Y. Tian. Adaptive Stabilization of Unstable Periodic Orbits of Chaotic Systems. Proceedings of the 3rd World Congress on Intelligent Control and Automation, Hefei, P.R.China, 2000:3195-3199
P. M. Alsing, A. Garielides. Using Neural Networks for Controlling Chaos. Phys. Rev. E, 1994,(49):1225-1231
C. T. Lin. Controlling Chaos by GA-based Reinforcement Learning Neural Network. IEEE Trans. on Neural Networks, 1999,(10):846-859
L. Chen, G. Chen Fuzzy Predictive Control of Uncertain Chaotic Systems Using Time Series. Int. J. Bif. and Chaos, 1999,9(4):757-767
X. Liu. Impulsive Control of Chaotic System. Int. J. Bif. and Chaos, 2002,12 (5):1181-1190
J. Sun, Y. Zhang. Impulsive Control of Systems. Phys. Lett. A, 2003, (306):306-312
B. R. N. Nbendjo, R. Tchoukuegno and P.Woafo. Active Control with Delay of Vibration and Chaos in a Double-well Duffing Oscillator. Chaos, Solitons and Fractals, 2003,18(2):773-792
S. Yang, C.Chen and H.Yau. Control of Chaos in Lorenz System. Chaos, Solitons and Fractals, 2002,13(4):773-792
H. Yau, C. Chen and C. Chen. Sliding Mode Control of Chaotic Systems with Uncertainties. Int. J. Bif. and Chaos, 2000,10(5):1139-1147
S. S. Ge, C. Wang and T. H. Lee. Adaptive Backstepping Control of a Class of Chaotic Systems. Int. J. Bif. and Chaos, 2000,10(5):1149-1156
T. Wu, Min-S. Chen. Chaos Control of the Modified Chua’s Circuit System. Physica D, 2002,164:53-58
L. M. Pecora, T. L. Carroll. Synchronization of Chaotic Systems. Phys. Rev. Lett. A,1990, (64):821-832
方锦清.非线性系统中混沌的控制与同步及其应用前景(二).物理学进展,1996, 16(2):137-196
J. A. K. Suykens, P. F. Curran. Robust Nonlinear Synchronization of Chaotic Lur’e System. IEEE Trans.on CAS., 1997,44(10):2031-2040
B. Michele, C. Donato. Synchronization of Hyper-chaotic Circuits via Continuous
Feedback Control with Application to Secure Communication. Int. J. Bif. and Chaos, 1998,8(10):2031-2040
C. Cruz, Synchronization through Filtering. Int. J. Bif. and Chaos, 2000, 10 (5):763-775
F. Liu., Y. Ren and X. Shan, et al. A Linear Feedback SynchronIzati on Theorem for a Class of Chaotic Systems. Chaos, Solitons and Fractals, 2002,13(4):723-730.
Y. Hong, H. Qin. Adaptive Synchronization of Chaotic systems via Output Feedback Control. Int. J. Bif. and Chaos, 2001,11(8):1149-1158
Y. Joo, L. Shieh and G. 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
H. Nijmeijer. A Dynamical Control View on Synchronization, Physica. D, 2001, (154):219-228
关新平,范正平,彭海朋.对一类具有随机扰动的混沌系统同步的新方法.电子学报, 2001,29(10):211-215
L. Kanellakopulos, P. V. Kokotovic and A. S. Morse. Systernatic Design of Adaptive Controllers for Feedback Linearizable Systems. IEEE Trans. on Automatic Control, 1991, 36(11):1241-1253
J. L, S. Zhang. Controlling Chen’s Chaotic Attractor Using Backstepping Design Based on Parameters Identification. Phys. Lett. A, 2001,(286):148-152
C. Wang, S. S. Ge. Adaptive Backstepping Control of Uncertain Lorenz System. Int. J. Bif. and Chaos, 2001,11(4):1115-1119
范正平,唐应干,关新平.一类混沌系统的鲁棒自适应控制研究.第14届控制与决策年会论文集.西安, 2001:50-53
S. S. Ge, C. Wang. Uncertain Chaotic System Control via Adaptive Neural Design. Int. J. Bif. and Chaos, 2002,12(5):1097-1109
宫琪,田玉平.非线性交叉严格反馈系统的一种构造性设计方法.自动化学报,2000, 26(4):447-453
王强德,陈卫田,魏春玲,等.一类不确定非线性系统的鲁棒自适应控制.控制理论与应用,2000,17(2):244-248
吴锋民,江春叶.Duffing方程的准混沌现象.浙江大学学报(自然科学版),1994, 21(3):339-340
刘宗华,方海平.Areneodo模型的研究.广西大学学报,1994,19(4):321-326
R. M. Sanner, J. E. Slotine. Gaussian Networks for Direct Adaptive Control. IEEE Trans. on Neural Networks, 1992,3(6):837-863
S. Chen, J. L. Synchronization of an Uncertain Unified Chaotic System via Adaptive Control. Chaos, Solitons and Fractals, 2002,14(3):643-647
G. Chen, U. Ueta. Yet Another Chaotic Attractor. Int. J. Bif. and Chaos, 1999, 9(7):1465-1466
关新平,彭海朋,李丽香等.Lorenz混沌系统的参数辨识与控制.物理学报,2001, 50(1):26-29
邹恩,李祥飞,陈建国.混沌控制及其优化应用.长沙:国防科技大学出版社,2002:32-33
方锦清.驾驭混沌与发展高新技术.北京:原子能出版社,2002:125, 239-248
L. Kocarev, U. Parisi. Generalized Synchronization, Predictability, and Equivalence of Unidirectionally Coupled Dynamical Systems. Phys. Rev. Lett.,1996,(76):1816-1819
J. Lu, Y. Xi. Linear Generalized Synchronization of Continuous-time Chaotic Systems. Chaos, Solitons and Fractals, 2003,17(5):825-831
郑大钟.线性系统理论.北京:清华大学出版社,1990:197
H. Nijmeijer, I. Mareels. An Observer Looks at Synchronization. IEEE Trans. on CAS., 1997,44(10):882-890
杨晓松.一类混沌系统观测器.物理学报,2000,49(10):1919-1203
U. Toshimitsu, Synthesis of Synchronized Chaotic Systems Based on Observers, Int. J. Bif. and Chaos, 1998,9(3):541-546
蒋国平,王锁平.基于状态观测器的超混沌系统同步方法研究,电子学报,2000, 28(1):108-110.
X. F. Wang, Z. Q. Wang, Synchronizing Chaos and Hyperchaos with Any Scalar Transmitted Signal, IEEE Trans. on CAS.,1998,45(10):1101-1103
马克茂,王子才,史小平.一类非线性系统的观测器设计.控制理论与应用,1998, 15(3):443-446
G. R. Duan. Solutions to Matrix Equation and Their Application to Eigen Structure Assignment in Linear Systems. IEEE Trans. on Automatic Control, 1993, 38(2):276-280
T. Matsumoto L. O. Chua and K. Kobayashi, et.al. Hyperchaos: Laboratory Experiment and Numerical Confirmation. IEEE Trans. on CAS., 1986,33(11):1143-1147
D. Koenig, S. Mammar. Design of a Class of Reduced Order Unknown Inputs Nonlinear Observer or Fault Diagnosis. Proceedings of the American Control Conference, Arlington,
VA, 2001:2143-2147
S. Magdi, Mahmoud. Robust control of Discrete Systems with Uncertain Parameters and Unknown Delays. Automatica, 2000,36(4): 627-635
T. Ushio, T. Innami S. Kodama. Chaos Shift Keying Based on In-phase and Anti-phase Chaotic Synchronization, IEICE Trans. Fundamental E79-A 10:1689-1693
G. Perez, H. A. Cerderra. Extracting Message Masked by Chaos. Phys. Rev. Lett. 1995, (74):1970-1973
M. K. Ali, J. Fang. Synchronization of Chaos and Hyperchaos Using Linear and Nonlinear Feedback Functions. Phys Rev E, 1997,(55):5285-5290
A. Namajunas. Analog Techniques for Modeling and Controlling the Mackey-Glass System. Int. J. Bif. and Chaos, 1998,8(7):957-962
F. Yang, R. W. Wilde. Observers for Linear Systems with Unknown Inputs. IEEE Trans. on Automatic. Control, 1988,33(6):677-681
L. H. Keel, S. P. Bhattacharyya. Robust Fragile or Optimal? IEEE Trans. on Automatic. Control, 1997,42(8):1098-1105
G. H. Yang, J. L. Wang and Y. C. Soh. Guaranteed Cost Control for Discrete-Time Linear Systems under Controller Gain Perturbations. Linear Algebra and its Applications, 2000, (312):161-180
D. Famularo, P. Dorato and C. T. Abdallah, et.al. Robust Non-Fragile LQ Controllers: the Static State Feedback Case, Int. J. Control, 2000,73(2): 159-165
邬晶.时滞系统的鲁棒稳定性分析与弹性控制器设计.[燕山大学硕士学位论文]. 2002:63-72
L. H. Keel S. P. Bhattacharyya. Author’s Reply. IEEE Trans. on Automatic Control. 1998, 43(9):1268
L. O. Chua. Chua’s Circuit-an Overview Ten Years Later. J Circuit Sys. Computer, 1994, (4):117-159
R. N. Madan. Chua’s Circuit:a Paradigm for Chaos. Singapore: World Scientific, 1993:34
K. Neal. A Course in Number and Theory and Cryptography. Spring-Verlag, 世界图书出版公司,1990:68
沈世镒,近代密码学.桂林:广西师范大学出版社,1999:78
W. Bender, D. Gruhl, and N. Morimoto. et.al.Techniques for Data Hiding. IBM System Journal, 1996,35(3):313-335
禹思敏,丘水生,罗伟民.混沌通信的研究进展与综合评述.桂林电子工业学院学报,
2000, 20(1):56-62
H. Fujisaka, T. Yamada. Stability Theory of Synchronized Motion in Coupled-oscillator Systems. Pro. Theo. Phys., 1983,(69):32-47
K.M. Cuomo, A. V. Oppenheim. Circuit Implementation of Synchronized Chaos with Application to Communications. Phys. Rev. Lett., 1993,(71):65-68
胡岗,萧井华,郑志刚.混沌控制.上海:上海科技教育出版社,2000:171-175
P. Yu, T. Lookman. Exact Recovery from Masked Chaotic Signal. Mini Symposium Cryptograghy, Toronto:Canadian Applied Mathematics Society, 1997:18-25
匡锦瑜,裴留庆.一种多级混沌同步通信系统.电子学报,1999,27(6):23-26
李建芬,李农.一种新的蔡氏混沌掩盖通信方法.系统工程与电子技术,2002,24(4):41-43
易开祥,孙鑫,石教英.一种基于混沌序列的图像加密算法.计算机辅助设计与图形学学报,2000,12(9):672-676
李昌刚,韩正之,张浩然.一种基于指数性混沌序列的灰度图像加密算法.计算机工程与应用,2001,(8):16-25
陆卫兵,彭建华,乔双.超混沌网络保密通讯软件的研究.东北师大学报(自然科学版), 2001,33(2):111-114
郝柏林.从抛物线谈起—混沌动力学引论.上海:上海科技教育出版社,1993:35
王光瑞,陈光旨.非线性常微分方程的混沌运动.南宁:广西科学技术出版社,1995:48
赵耿,郑德玲,方锦清.混沌保密通信的最新进展.自然杂志,23(2):97-107
攻读硕士学位期间参加的科研课题
“时滞混沌系统的控制和同步研究”,国家自然科学基金,( No:60274023)
“混沌保密通信技术及应用研究”,河北省自然科学基金,( No: 601225)
攻读硕士学位期间的科学研究成果
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
关新平,何宴辉，范正平等.一类参数未知混沌系统的鲁棒自适应控制.控制与决策, 2003,18(3):324-327
关新平,何宴辉,邬晶.基于弹性控制器的混沌同步.物理学报, 2003,52(11): 2718-2722
关新平,何宴辉,唐英干.随机扰动下一类混沌系统的同步.系统工程与电子技术(待发表)
何宴辉,范正平,关新平.一类混沌系统基于观测器的鲁棒同步控制.第14届控制与决策年会论文集,西安, 2002:65-69
关新平,何宴辉.扰动下连续时滞混沌系统的线性广义同步.中国矿大博士后讲坛
Guan Xinping, He Yanhui. Stabilizing UEP of Unified Chaotic System with Unknown Parameter Using Sliding Mode Control. Chinese Physics Letters. 2004,21(2):227-229
He Yanhui, Chen Cailian, Liu Tongshuan, Guan Xinping. Adaptive Backstepping Control of a Chaotic System Using RBF Neural Networks. IEEE Intelligent Automation Conference, Hong Kong, 2003:68-71
关新平,彭海朋,何宴辉.具有随机扰动连续时滞混沌系统的同步.系统工程与电子技术, 2002, 24(9):74-77
关新平,范正平,何宴辉.混沌控制综述.燕山大学学报(中国自动化学会,2001,北戴河学术年会专刊), 25:1-4