混沌系统基于T-S模糊模型的最优控制研究
|
摘要
研究混沌系统的控制不仅具有高度的理论价值,也具有深远的实际意义。自从人们发现混沌系统可以被控制以后,混沌系统的控制研究便受到了高度的重视,随后有关混沌系统控制的许多方法也不断的被提出。基于已有的控制理论,本文针对混沌系统的镇定控制和跟踪控制这两个问题做了一些工作,主要研究内容如下:
首先,研究了连续混沌系统的镇定控制问题,由于混沌系统的非线性特性,直接应用最优控制理论实现连续混沌系统的控制很困难,本文考虑对混沌系统进行基于T-S模糊模型建模,通过建模后,可以针对局部线性子系统分别设计最优控制器,进而达到对混沌系统的控制,通过对Chen系统和超混沌Lorenz系统的控制仿真实验验证了该方法的控制效果。
其次,研究了离散混沌系统的镇定控制问题,和连续混沌系统相似,离散混沌系统直接应用最优控制理论实现对其控制也是很困难的,本文首先利用离散系统的基于T-S模糊模型建模的方法,对离散混沌系统进行建模,然后利用最优控制理论中的离散系统的最优状态控制器设计方法,对系统进行控制器设计,以Hénon系统及广义Hénon系统的镇定控制仿真实验来验证了该方法控制效果。
最后,研究了混沌系统的跟踪控制问题,为了实现受控制系统对期望混沌系统的跟踪,先提出对受控混沌系统与期望混沌系统进行基于T-S模糊模型的建模,接着根据建模后的局部子系统的对应关系,通过增广向量和增广矩阵表示后,将受控混沌系统与期望混沌系统联系起来,利用最优输出调节器的设计方法对每个系统进行控制器的设计,然后,通过对相同结构不同初始状态和不同结构不同初始状态的混沌系统的控制仿真实验证实了该方法的性能。
The study of chaotic control not only is a high degree of theoretical value, but also has far-reaching practical significance. Since it is found that the chaotic systems can be controlled, the control of chaotic systems is attracting great attention, many methods of chaotic control are constantly proposed. Based on the theory,in this paper, the problems of the stabilization control of chaotic systems and the tracking control of chaotic systems are studied. The details are clarified as follows:
Firstly, the stabilization control of the continuous chaotic system is studied, because of the nonlinear characteristics of chaotic systems, it is hard to directly use optimal control theory for the continuous chaos control, at first, to solve this problem, TS fuzzy model is used for chaotic system modeling in this paper, thus, optimal controller can be designed for local linear subsystems, and the chaotic system is controlled. The effective of the control method is confirmed by the simulation experiments of the Chen system and hyperchaotic Lorenz system.
Secondly, the stabilization control of the discrete chaotic system is studied; And similar to continuous chaotic system, it is also difficult to directly using optimal control theory for controlling discrete chaos, in this paper, first of all, the discrete chaotic system is modeled based on TS fuzzy model, then, the optimal controller of every linear discrete subsystem is designed on the optimal control theory of discrete systems, thus the controller of the discrete chaotic system is designed, simulation experiments of the generalized Hénon system and Hénon system show the effectiveness of the method.
Finally, the tracking control problem of chaotic systems is studied, in order to let a controlled system track the expected chaotic system, firstly, the two chaotic systems are modeled based on TS fuzzy model, then, according to the connection among the subsystems, the two chaotic systems are connected by the augmented vector and augmented matrix, thus, the optimal output controller of each system is designed on optimal control theory, simulation experiments of chaotic systems of the same structure with different initial states and chaotic systems of different structures with different initial states of with different initial states verify the effective of the method.
首先,研究了连续混沌系统的镇定控制问题,由于混沌系统的非线性特性,直接应用最优控制理论实现连续混沌系统的控制很困难,本文考虑对混沌系统进行基于T-S模糊模型建模,通过建模后,可以针对局部线性子系统分别设计最优控制器,进而达到对混沌系统的控制,通过对Chen系统和超混沌Lorenz系统的控制仿真实验验证了该方法的控制效果。
其次,研究了离散混沌系统的镇定控制问题,和连续混沌系统相似,离散混沌系统直接应用最优控制理论实现对其控制也是很困难的,本文首先利用离散系统的基于T-S模糊模型建模的方法,对离散混沌系统进行建模,然后利用最优控制理论中的离散系统的最优状态控制器设计方法,对系统进行控制器设计,以Hénon系统及广义Hénon系统的镇定控制仿真实验来验证了该方法控制效果。
最后,研究了混沌系统的跟踪控制问题,为了实现受控制系统对期望混沌系统的跟踪,先提出对受控混沌系统与期望混沌系统进行基于T-S模糊模型的建模,接着根据建模后的局部子系统的对应关系,通过增广向量和增广矩阵表示后,将受控混沌系统与期望混沌系统联系起来,利用最优输出调节器的设计方法对每个系统进行控制器的设计,然后,通过对相同结构不同初始状态和不同结构不同初始状态的混沌系统的控制仿真实验证实了该方法的性能。
The study of chaotic control not only is a high degree of theoretical value, but also has far-reaching practical significance. Since it is found that the chaotic systems can be controlled, the control of chaotic systems is attracting great attention, many methods of chaotic control are constantly proposed. Based on the theory,in this paper, the problems of the stabilization control of chaotic systems and the tracking control of chaotic systems are studied. The details are clarified as follows:
Firstly, the stabilization control of the continuous chaotic system is studied, because of the nonlinear characteristics of chaotic systems, it is hard to directly use optimal control theory for the continuous chaos control, at first, to solve this problem, TS fuzzy model is used for chaotic system modeling in this paper, thus, optimal controller can be designed for local linear subsystems, and the chaotic system is controlled. The effective of the control method is confirmed by the simulation experiments of the Chen system and hyperchaotic Lorenz system.
Secondly, the stabilization control of the discrete chaotic system is studied; And similar to continuous chaotic system, it is also difficult to directly using optimal control theory for controlling discrete chaos, in this paper, first of all, the discrete chaotic system is modeled based on TS fuzzy model, then, the optimal controller of every linear discrete subsystem is designed on the optimal control theory of discrete systems, thus the controller of the discrete chaotic system is designed, simulation experiments of the generalized Hénon system and Hénon system show the effectiveness of the method.
Finally, the tracking control problem of chaotic systems is studied, in order to let a controlled system track the expected chaotic system, firstly, the two chaotic systems are modeled based on TS fuzzy model, then, according to the connection among the subsystems, the two chaotic systems are connected by the augmented vector and augmented matrix, thus, the optimal output controller of each system is designed on optimal control theory, simulation experiments of chaotic systems of the same structure with different initial states and chaotic systems of different structures with different initial states of with different initial states verify the effective of the method.
引文
1陈关荣,吕金虎. Lorenz系统族的动力学分析、混沌控制与同步.北京:科学出版社, 2003:1-8
2曹建福,韩崇昭,方洋旺.非线性系统理论及应用.西安:西安交通大学出版社, 2001:73-82
3王兴元.复杂非线性系统中的混沌.北京:电子工业出版社, 2003:2-3
4 E. N. Lorenz. Deterministic Nonperiodic Flow. J. Atmos. Sci., 1963, 20:130-141
5 R. M. May. Simple Mathematical Models with Very Complicated Dynamics. Nature, 1976, 261:959-967
6赵耿,郑德玲,张亦舜.混沌学及混沌电子学的发展.原子能科学技术, 2002, 36(3):284-289
7 A. W. Hubler, E. Luscher. Resonant Stimulation and Control of Nonlinear Oscillators. Naturwissenschaft 76, 1989:67
8 A. W. Hubler. Adaptive Control of Chaotic Systems. Helvetica Physica Acta, 1989, 62: 343-346
9 W. L. Ditto, S. N. Rauseo, M. L. Spano. Experimental Control of Chaos. Phys. Rev. Lett. 1990, (65): 3211-3214
10 R. Roy, T. W. Murphy, T. D. Maier, et al. Dynamical Control of a Chaotic Laser: Experimental Stabilization of a Globally Coupled System. Phys. Rev. Lett., 1992, (68): 1259-1262
11张雨.时间序列的混沌和符号分析及实践.长沙:国防科技大学出版社, 2007: 16-17
12 E. Ott, C. Grebogi, J. A. Yorke. Controlling Chaos. Physical Review Letters, 1990, 64(11):1196-1199
13关新平,范正平,陈彩莲,等.混沌控制及其在保密通信中的应用.北京:国防工业出版社, 2002:22-30
14 U. Dressler, G. Nitsche. Controlling Chaos Using Time Delay Coordinates. Phys.Rev. Lett., 1992, 68(1):1261-1264
15 F. J. Romeiras, E. Ott, C. Grebogi, et al. Controlling Chaotic Dynamical Systems. Phys. D., 1992, 58:165-192
16 P. Yadmellat, S. Kamaleddin, Y. Nikravesh. A Recursive Delayed Output-feedback Control to Stabilize Chaotic Systems Using Linear-in-parameter Neural Networks. Commun Nonlinear Sci Numer Simulat, 2010, 16(2011):383-394
17 M. Roopaei, B. R. Sahraei, T. C. Lin. Adaptive Sliding Mode Control in a Novel Class of Chaotic Systems. Commun Nonlinear Sci Numer Simulat, 2010, 15:4158-4170
18 K. Merat, H. Salarieh, A. Alasty. Implementation of Dynamic Programming for Chaos Control in Discrete Systems. Journal of Computational and Applied Mathematics, 2010, 233:531-544
19 P. R. Agarwal, H. Yu, S. Zhong. Mathematics Analysis and Chaos in an Ecological Model with an Impulsive Control Strategy. Commun Nonlinear Sci Numer Simulat, 2010, 16:776-786
20 M. Sadeghpour, H. Salarieh, G. Vossoughi, et al. Multi-variable Control of Chaos Using PSO-based Minimum Entropy Control. Commun Nonlinear Sci Numer Simulat, 2010, doi:10.1016/j.cnsns.2010.09.019
21 N. Noroozi, M. Roopaei, P. Karimaghaee, et al. Simple Adaptive Variable Structure Control for Unknown Chaotic Systems. Commun Nonlinear Sci Numer Simulat, 2010, 15:707-727
22 A. Loría. Control of the New 4th-order Hyper-chaotic System with One Input. Commun Nonlinear Sci Numer Simulat, 2010, 15:1621-1630
23 J. Baek. Adaptive Fuzzy Bilinear Feedback Control Design for Synchronization of TS Fuzzy Bilinear Generalized Lorenz System with Uncertain Parameters. Physics Letters A, 2010, 374:1827-1834
24 S. Dadras, H. R. Momeni. Adaptive Sliding Mode Control of Chaotic Dynamical Systems with Application to Synchronization. Mathematics and Computers in Simulation, 2010, 80:2245-2257
25 S. H. Hosseinnia, R. Ghaderi, A. N. Ranjbar, et al. Sliding Mode Synchronization of an Uncertain Fractional Order Chaotic System. Computers and Mathematics with Applications, 2010, 59:1637-1643
26 M. Gamal Mahmoud, E. Emad Mahmoud. Synchronization and Control of Hyperchaotic Complex Lorenz System. Mathematics and Computers in Simulation, 2010, 80:2286-2296
27 A. N. Njah, K. S. Ojo, G. A. Adebayo, et al. Generalized Control and Synchronization of Chaos in RCL-shunted Josephson Junction Using Backstepping Design. Physica C, 2010, 470: 558-564
28 M. Shahiri, R. Ghaderi, A. N. Ranjbar, et al. Chaotic Fractional-order Coullet System: Synchronization and Control Approach. Commun Nonlinear Sci Numer Simulat, 2010, 15:665-674
29 K. Sebastian Sudheer, M. Sabir. Switched Modified Function Projective Synchronization of Hyperchaotic Qi System with Uncertain Parameters. Commun Nonlinear Sci Numer Simulat, 2010, 15:4058-4064
30路永坤,夏超英.改进变论域模糊控制及其在混沌系统中的应用.天津大学学报, 2010, 43(8):749-754
31吴然超,郭玉祥.含一个非线性项混沌系统的线性控制及反控制.物理学报, 2010, 59(8):5293-5298
32陈帝伊,陈海涛,马孝义,等.只含一个非线性项的超混沌系统及其控制比较.计算机应用, 2010, 30(8):2045-2048
33陈光平,张志远,郝加波. Chen氏混沌系统的周期扰动控制.四川师范大学学报(自然科学版), 2010, 33(4):563-567
34高大威,崔玲,王昊.追踪控制双频激励下汽车悬架系统的混沌运动.振动与冲击, 2010, 29(5):58-61
35阎晓妹,刘丁.基于观测器的不确定超混沌Lü系统的主动控制.西安理工大学学报, 2010, 26(1):1-6
36徐玉华,周武能.一类新单参数混沌系统的降维控制.东华大学学报(自然科学版), 2010, 36(1):52-56
37李目,周少武,何怡刚,等.不确定混沌系统的差分进化小波神经网络控制.计算机工程与应用, 2010, 46(11):200-204
38付景超,井元伟,张嗣瀛.一类离散功能性反应模型的混沌跟踪控制.控制与决策, 2010, 25(3):466-468
39朱少平,钱富才,刘丁.不确定动态混沌系统的最优控制.物理学报, 2010, 59(4):2250-2254
40王新,马义德,徐志坚,等.基于脉冲耦合神经网络的混沌控制.计算机应用, 2009, 29(12):3277-3279
41孙宁,张化光,王智良.不确定分数阶混沌系统的滑模投影同步.浙江大学学报(工学版), 2010, 44(7):1288-1291
42付士慧,裴利军.具有非线性控制的Chua电路的混沌同步.物理学报, 2010, 59(9):5985-5990
43王宏伟,于双和.基于Chebyshev正交函数神经网络的混沌系统鲁棒自适应同步.控制理论与应用, 2009,26(10):1100-1104
44杨东升,张化光,赵琰,等.基于LMI的参数未知时变时滞混沌系统模糊自适应H∞同步.物理学报, 2010, 59(3):15062-1568
45唐良瑞,左琪.基于超混沌系统的正交频分复用时频同步算法.中国电机工程学报, 2010, 30(12):122-129
46冯秀琴,姚治海,田作林,等.简并光学参量振荡器的混沌反控制与混沌同步.光学学报, 2010, 30(3):861-865
47王健安,李壮举,刘贺平.四维混沌系统的自适应修正函数投影同步.系统工程与电子技术, 2010, 32(8):1745-1749
48吕翎,李钢,商锦玉,等.最近邻耦合网络的时空混沌同步研究.物理学报, 2010, 59(9):5966-5972
49聂春燕.混沌系统与弱信号检测.北京:清华大学出版社, 2009:9-11
50黄润生,黄浩.混沌及其应用.武汉:武汉大学出版社, 2005:118-123
51项国波.非线性系统.北京:知识出版社, 1991:1-3
52 E. H. Mamdani, S. Assilian. An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller. Int. J. Man Math. Studies, 1975, 7(1):1-13
53 Y. Tsukamoto. An Approach to Fuzzy Reasoning Method. In: Madan M. Gupta, Rammohan K. Ragade, Ronald R. Yager, Eds. In Advances in Fuzzy Set Theory and Applications, Amsterdam: North-Holland, 1979:137-149
54廖倩芳.Ⅱ型T-S模糊建模与控制. [上海交通大学硕士论文]. 2009:4-5
55 T. Takagi, M. Sugeno. Fuzzy Identification of Systems and ItsApplications to Modeling and Control. IEEE Transaction on Systems, 1985, 15(1):116-132
56胡寿松,王执铨,胡维礼.最优控制理论与系统.北京:科学出版社, 2005:2-220
57刘芬,王仁明,曾晓,等. Chen混沌系统的模糊控制.计算机仿真, 2007, 24(3):149-152
58钱俊磊,马晓峰,杨志刚.混沌系统基于T-S模糊模型的控制方法.系统仿真学报, 2005,17(12):2987-2991
59赵琰,邓玮,王智良.基于精确线性化的Nadolschi混沌系统T-S模糊控制.计算机应用技术, 2009, 8:63-66
60宋运忠,赵光宙,齐冬莲.统一混沌系统的最优控制.系统仿真学报, 2007, 19(1):123-125
61赵明旺,王杰,汪卫华.现代控制理论.武汉:华中科技大学出版社, 2007:131-198
62 G. Chen, C. J. Tian, Y. M. Shi. Stability and Chaos in 2-D Discrete Systems. Chaos Solitons Fractals, 2005, 25:637-647
63 C. J. Tian, G. Chen. Stability for Delayed Generalized 2-D Discrete Logistic Systems. Adv. Difference Equ., 2004, 4:279-290
64 H. Salarieh, M. Shahrokhi. Indirect Adaptive Control of Discrete Chaotic Systems. Chaos Soliton Fract, 2007, 34:1188-1201
65 D. J. Christini, J. J. Collins. Real-time, Adaptive, Model-independent Control of Low-dimensional Chaotic and Non-chaotic Dynamical Systems. IEEE Trans. Circ. Sys., 1997, 44:1027-1030
66 K. Merat, H. Salarieh, A. Alasty. Implementation of Dynamic Programming for Chaos Control in Discrete Systems. Journal of Computational and Applied Mathematics, 2009, 233:531-544
67刘丁,钱富才,任海鹏,等.离散混沌系统的最小能量控制.物理学报, 2004,53(7):2074-2080
68 D. Lin, X. Wang, F. Z. Nian, et al. Dynamic Fuzzy Neural Networks Modeling and Adaptive Backstepping Tracking Control of Uncertain Chaotic Systems. Neurocomputing (2010), doi:10.1016/j.neucom.2010.08.008
69 N. Noroozi, M. Roopaei, P. Karimaghaee. Simple Adaptive Variable Structure Control for Unknown Chaotic Systems. Commun Nonlinear Sci Numer Simulat, 2010, 15:707-727
70贺乃宝,姜长生,高倩.非线性混沌系统的鲁棒自适应控制.重庆大学学报, 2009, 32(1):96-99
71刘亚,胡寿松.基于自适应神经网络的不确定非线性系统的模糊跟踪控制.控制理论与应用, 2004, 21(5):770-775
72王兴元,王明军.超混沌Lorenz系统.物理学报, 2007, 56(9):5136-5141
73 M. A. Hénon. Two Dimensional Map with a Strange Attractor. Commun Math Phys, 1976, 50(1):69-73
74尹逊和,任勇,山秀明.广义Hénon映射的滑模变结构控制同步.物理学报, 2002, 51(9):1949-1953
75杨志红,常凤云,姚琼荟.基于T-S模糊模型的离散混沌系统变结构控制.控制工程, 2007, 14(2):161-163
2曹建福,韩崇昭,方洋旺.非线性系统理论及应用.西安:西安交通大学出版社, 2001:73-82
3王兴元.复杂非线性系统中的混沌.北京:电子工业出版社, 2003:2-3
4 E. N. Lorenz. Deterministic Nonperiodic Flow. J. Atmos. Sci., 1963, 20:130-141
5 R. M. May. Simple Mathematical Models with Very Complicated Dynamics. Nature, 1976, 261:959-967
6赵耿,郑德玲,张亦舜.混沌学及混沌电子学的发展.原子能科学技术, 2002, 36(3):284-289
7 A. W. Hubler, E. Luscher. Resonant Stimulation and Control of Nonlinear Oscillators. Naturwissenschaft 76, 1989:67
8 A. W. Hubler. Adaptive Control of Chaotic Systems. Helvetica Physica Acta, 1989, 62: 343-346
9 W. L. Ditto, S. N. Rauseo, M. L. Spano. Experimental Control of Chaos. Phys. Rev. Lett. 1990, (65): 3211-3214
10 R. Roy, T. W. Murphy, T. D. Maier, et al. Dynamical Control of a Chaotic Laser: Experimental Stabilization of a Globally Coupled System. Phys. Rev. Lett., 1992, (68): 1259-1262
11张雨.时间序列的混沌和符号分析及实践.长沙:国防科技大学出版社, 2007: 16-17
12 E. Ott, C. Grebogi, J. A. Yorke. Controlling Chaos. Physical Review Letters, 1990, 64(11):1196-1199
13关新平,范正平,陈彩莲,等.混沌控制及其在保密通信中的应用.北京:国防工业出版社, 2002:22-30
14 U. Dressler, G. Nitsche. Controlling Chaos Using Time Delay Coordinates. Phys.Rev. Lett., 1992, 68(1):1261-1264
15 F. J. Romeiras, E. Ott, C. Grebogi, et al. Controlling Chaotic Dynamical Systems. Phys. D., 1992, 58:165-192
16 P. Yadmellat, S. Kamaleddin, Y. Nikravesh. A Recursive Delayed Output-feedback Control to Stabilize Chaotic Systems Using Linear-in-parameter Neural Networks. Commun Nonlinear Sci Numer Simulat, 2010, 16(2011):383-394
17 M. Roopaei, B. R. Sahraei, T. C. Lin. Adaptive Sliding Mode Control in a Novel Class of Chaotic Systems. Commun Nonlinear Sci Numer Simulat, 2010, 15:4158-4170
18 K. Merat, H. Salarieh, A. Alasty. Implementation of Dynamic Programming for Chaos Control in Discrete Systems. Journal of Computational and Applied Mathematics, 2010, 233:531-544
19 P. R. Agarwal, H. Yu, S. Zhong. Mathematics Analysis and Chaos in an Ecological Model with an Impulsive Control Strategy. Commun Nonlinear Sci Numer Simulat, 2010, 16:776-786
20 M. Sadeghpour, H. Salarieh, G. Vossoughi, et al. Multi-variable Control of Chaos Using PSO-based Minimum Entropy Control. Commun Nonlinear Sci Numer Simulat, 2010, doi:10.1016/j.cnsns.2010.09.019
21 N. Noroozi, M. Roopaei, P. Karimaghaee, et al. Simple Adaptive Variable Structure Control for Unknown Chaotic Systems. Commun Nonlinear Sci Numer Simulat, 2010, 15:707-727
22 A. Loría. Control of the New 4th-order Hyper-chaotic System with One Input. Commun Nonlinear Sci Numer Simulat, 2010, 15:1621-1630
23 J. Baek. Adaptive Fuzzy Bilinear Feedback Control Design for Synchronization of TS Fuzzy Bilinear Generalized Lorenz System with Uncertain Parameters. Physics Letters A, 2010, 374:1827-1834
24 S. Dadras, H. R. Momeni. Adaptive Sliding Mode Control of Chaotic Dynamical Systems with Application to Synchronization. Mathematics and Computers in Simulation, 2010, 80:2245-2257
25 S. H. Hosseinnia, R. Ghaderi, A. N. Ranjbar, et al. Sliding Mode Synchronization of an Uncertain Fractional Order Chaotic System. Computers and Mathematics with Applications, 2010, 59:1637-1643
26 M. Gamal Mahmoud, E. Emad Mahmoud. Synchronization and Control of Hyperchaotic Complex Lorenz System. Mathematics and Computers in Simulation, 2010, 80:2286-2296
27 A. N. Njah, K. S. Ojo, G. A. Adebayo, et al. Generalized Control and Synchronization of Chaos in RCL-shunted Josephson Junction Using Backstepping Design. Physica C, 2010, 470: 558-564
28 M. Shahiri, R. Ghaderi, A. N. Ranjbar, et al. Chaotic Fractional-order Coullet System: Synchronization and Control Approach. Commun Nonlinear Sci Numer Simulat, 2010, 15:665-674
29 K. Sebastian Sudheer, M. Sabir. Switched Modified Function Projective Synchronization of Hyperchaotic Qi System with Uncertain Parameters. Commun Nonlinear Sci Numer Simulat, 2010, 15:4058-4064
30路永坤,夏超英.改进变论域模糊控制及其在混沌系统中的应用.天津大学学报, 2010, 43(8):749-754
31吴然超,郭玉祥.含一个非线性项混沌系统的线性控制及反控制.物理学报, 2010, 59(8):5293-5298
32陈帝伊,陈海涛,马孝义,等.只含一个非线性项的超混沌系统及其控制比较.计算机应用, 2010, 30(8):2045-2048
33陈光平,张志远,郝加波. Chen氏混沌系统的周期扰动控制.四川师范大学学报(自然科学版), 2010, 33(4):563-567
34高大威,崔玲,王昊.追踪控制双频激励下汽车悬架系统的混沌运动.振动与冲击, 2010, 29(5):58-61
35阎晓妹,刘丁.基于观测器的不确定超混沌Lü系统的主动控制.西安理工大学学报, 2010, 26(1):1-6
36徐玉华,周武能.一类新单参数混沌系统的降维控制.东华大学学报(自然科学版), 2010, 36(1):52-56
37李目,周少武,何怡刚,等.不确定混沌系统的差分进化小波神经网络控制.计算机工程与应用, 2010, 46(11):200-204
38付景超,井元伟,张嗣瀛.一类离散功能性反应模型的混沌跟踪控制.控制与决策, 2010, 25(3):466-468
39朱少平,钱富才,刘丁.不确定动态混沌系统的最优控制.物理学报, 2010, 59(4):2250-2254
40王新,马义德,徐志坚,等.基于脉冲耦合神经网络的混沌控制.计算机应用, 2009, 29(12):3277-3279
41孙宁,张化光,王智良.不确定分数阶混沌系统的滑模投影同步.浙江大学学报(工学版), 2010, 44(7):1288-1291
42付士慧,裴利军.具有非线性控制的Chua电路的混沌同步.物理学报, 2010, 59(9):5985-5990
43王宏伟,于双和.基于Chebyshev正交函数神经网络的混沌系统鲁棒自适应同步.控制理论与应用, 2009,26(10):1100-1104
44杨东升,张化光,赵琰,等.基于LMI的参数未知时变时滞混沌系统模糊自适应H∞同步.物理学报, 2010, 59(3):15062-1568
45唐良瑞,左琪.基于超混沌系统的正交频分复用时频同步算法.中国电机工程学报, 2010, 30(12):122-129
46冯秀琴,姚治海,田作林,等.简并光学参量振荡器的混沌反控制与混沌同步.光学学报, 2010, 30(3):861-865
47王健安,李壮举,刘贺平.四维混沌系统的自适应修正函数投影同步.系统工程与电子技术, 2010, 32(8):1745-1749
48吕翎,李钢,商锦玉,等.最近邻耦合网络的时空混沌同步研究.物理学报, 2010, 59(9):5966-5972
49聂春燕.混沌系统与弱信号检测.北京:清华大学出版社, 2009:9-11
50黄润生,黄浩.混沌及其应用.武汉:武汉大学出版社, 2005:118-123
51项国波.非线性系统.北京:知识出版社, 1991:1-3
52 E. H. Mamdani, S. Assilian. An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller. Int. J. Man Math. Studies, 1975, 7(1):1-13
53 Y. Tsukamoto. An Approach to Fuzzy Reasoning Method. In: Madan M. Gupta, Rammohan K. Ragade, Ronald R. Yager, Eds. In Advances in Fuzzy Set Theory and Applications, Amsterdam: North-Holland, 1979:137-149
54廖倩芳.Ⅱ型T-S模糊建模与控制. [上海交通大学硕士论文]. 2009:4-5
55 T. Takagi, M. Sugeno. Fuzzy Identification of Systems and ItsApplications to Modeling and Control. IEEE Transaction on Systems, 1985, 15(1):116-132
56胡寿松,王执铨,胡维礼.最优控制理论与系统.北京:科学出版社, 2005:2-220
57刘芬,王仁明,曾晓,等. Chen混沌系统的模糊控制.计算机仿真, 2007, 24(3):149-152
58钱俊磊,马晓峰,杨志刚.混沌系统基于T-S模糊模型的控制方法.系统仿真学报, 2005,17(12):2987-2991
59赵琰,邓玮,王智良.基于精确线性化的Nadolschi混沌系统T-S模糊控制.计算机应用技术, 2009, 8:63-66
60宋运忠,赵光宙,齐冬莲.统一混沌系统的最优控制.系统仿真学报, 2007, 19(1):123-125
61赵明旺,王杰,汪卫华.现代控制理论.武汉:华中科技大学出版社, 2007:131-198
62 G. Chen, C. J. Tian, Y. M. Shi. Stability and Chaos in 2-D Discrete Systems. Chaos Solitons Fractals, 2005, 25:637-647
63 C. J. Tian, G. Chen. Stability for Delayed Generalized 2-D Discrete Logistic Systems. Adv. Difference Equ., 2004, 4:279-290
64 H. Salarieh, M. Shahrokhi. Indirect Adaptive Control of Discrete Chaotic Systems. Chaos Soliton Fract, 2007, 34:1188-1201
65 D. J. Christini, J. J. Collins. Real-time, Adaptive, Model-independent Control of Low-dimensional Chaotic and Non-chaotic Dynamical Systems. IEEE Trans. Circ. Sys., 1997, 44:1027-1030
66 K. Merat, H. Salarieh, A. Alasty. Implementation of Dynamic Programming for Chaos Control in Discrete Systems. Journal of Computational and Applied Mathematics, 2009, 233:531-544
67刘丁,钱富才,任海鹏,等.离散混沌系统的最小能量控制.物理学报, 2004,53(7):2074-2080
68 D. Lin, X. Wang, F. Z. Nian, et al. Dynamic Fuzzy Neural Networks Modeling and Adaptive Backstepping Tracking Control of Uncertain Chaotic Systems. Neurocomputing (2010), doi:10.1016/j.neucom.2010.08.008
69 N. Noroozi, M. Roopaei, P. Karimaghaee. Simple Adaptive Variable Structure Control for Unknown Chaotic Systems. Commun Nonlinear Sci Numer Simulat, 2010, 15:707-727
70贺乃宝,姜长生,高倩.非线性混沌系统的鲁棒自适应控制.重庆大学学报, 2009, 32(1):96-99
71刘亚,胡寿松.基于自适应神经网络的不确定非线性系统的模糊跟踪控制.控制理论与应用, 2004, 21(5):770-775
72王兴元,王明军.超混沌Lorenz系统.物理学报, 2007, 56(9):5136-5141
73 M. A. Hénon. Two Dimensional Map with a Strange Attractor. Commun Math Phys, 1976, 50(1):69-73
74尹逊和,任勇,山秀明.广义Hénon映射的滑模变结构控制同步.物理学报, 2002, 51(9):1949-1953
75杨志红,常凤云,姚琼荟.基于T-S模糊模型的离散混沌系统变结构控制.控制工程, 2007, 14(2):161-163