基于细胞神经网络保密通信研究
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摘要
细胞神经网络(Cellular Neural Networks,简称CNN)动力学是神经网络与动力学系统交叉结合的一门新型学科,它的理论和应用研究成了当前的研究热点。CNN是一个高速非线性动力学系统,不同的模板参数选择表现出复杂的动力学行为,在满足一定条件下,系统会出现分岔和混沌现象。由于混沌系统具有对初始条件和系统模板参数的高度敏感性,是伪随机系列的天然候选者,这为CNN在保密通信中的应用提供了可靠的理论基础。本文在研究CNN的稳定性前提下,分析系统的动力学行为,设计出合适的CNN混沌与超混沌模板参数,并将其应用于保密通信中,主要研究成果体现在:
(1)运用Lipschittz连续条件、不动点定理、Lyapunov函数稳定理及不等式方法,分析了CNN的全局渐近稳定性,设计推导的稳定性判断标准为不等式表达式,简单实用,对CNN邻域内细胞间相互作用为线性的稳定性分析具有通用性。
(2)根据Lyapunov第一近似理论分析了CNN邻域内细胞间相互作用为非线性的稳定性情况,所采用的判断方法对全互连CNN模型的构造与稳定性分析具有通用性。
(3)结合CNN稳定性判断方法构造了CNN混沌与高维超混沌系统,应用于音频保密通信中,实现了收发端的同步,使原始信号在接收端得到了较好的恢复。
(4)设计了基于五维CNN全维和降维状态观测器的超混沌同步系统,通过仿真与数值测试得出:如果CNN超混沌系统的状态变量差值保持在一定范围内,可以较精确实现保密通信。
Cellular Neural Networks (CNN) dynamics is a new kind of interdisciplinary sciences combined with neural networks and dynamic system, the theory and application of CNN have become a new focus recently. It is known that the CNN is a nonlinear dynamic system with high speed, different parameters selection for system template will lead to different dynamic behaviors such as bifurcation phenomenon and chaotic character, which provide reliable theory basis for secure communication because chaotic systems have a high sensitivity for changes of system initial conditions and template parameters. In this thesis, we gave attentions to the researches of CNN’s stability and nonlinear dynamic behaviors. At the same time, we designed some good template parameters for CNN application in secure communication. Main research works are shown as follows.
Firstly, a novel criterion for CNN’s global asymptotic stability analysis is derived based on Lipschitz condition, fixed point theory and Lyapunov functional stability analysis. It is expressed by inequality equations and is universal for CNN’s stability judgment when the interaction between cells is linear. Some numerical examples are given to show the effectiveness.
Secondly, we have applied the first method of Lyapunov to analyze CNN’s stability when the interaction between cells is nonlinear. Another novel criterion for the global asymptotic stability of cellular neural networks has been adopted with eigen-values analysis for Lyapunov’s linear-matrix, it is feasible by experiment test.
Thirdly, a 5-order CNN hyper-chaotic system is designed according to the criterions put forward above, and it is applied to secure communication.
Fourthly, we have constructed CNN chaotic and hyper-chaotic secure communication system based on the theories for chaos synchronization and state observer, a new technical requirement has been proposed: if the state values of CNN can be arbitrarily controlled within a certain control-range, the secure communication can be realized precisely.
(1)运用Lipschittz连续条件、不动点定理、Lyapunov函数稳定理及不等式方法,分析了CNN的全局渐近稳定性,设计推导的稳定性判断标准为不等式表达式,简单实用,对CNN邻域内细胞间相互作用为线性的稳定性分析具有通用性。
(2)根据Lyapunov第一近似理论分析了CNN邻域内细胞间相互作用为非线性的稳定性情况,所采用的判断方法对全互连CNN模型的构造与稳定性分析具有通用性。
(3)结合CNN稳定性判断方法构造了CNN混沌与高维超混沌系统,应用于音频保密通信中,实现了收发端的同步,使原始信号在接收端得到了较好的恢复。
(4)设计了基于五维CNN全维和降维状态观测器的超混沌同步系统,通过仿真与数值测试得出:如果CNN超混沌系统的状态变量差值保持在一定范围内,可以较精确实现保密通信。
Cellular Neural Networks (CNN) dynamics is a new kind of interdisciplinary sciences combined with neural networks and dynamic system, the theory and application of CNN have become a new focus recently. It is known that the CNN is a nonlinear dynamic system with high speed, different parameters selection for system template will lead to different dynamic behaviors such as bifurcation phenomenon and chaotic character, which provide reliable theory basis for secure communication because chaotic systems have a high sensitivity for changes of system initial conditions and template parameters. In this thesis, we gave attentions to the researches of CNN’s stability and nonlinear dynamic behaviors. At the same time, we designed some good template parameters for CNN application in secure communication. Main research works are shown as follows.
Firstly, a novel criterion for CNN’s global asymptotic stability analysis is derived based on Lipschitz condition, fixed point theory and Lyapunov functional stability analysis. It is expressed by inequality equations and is universal for CNN’s stability judgment when the interaction between cells is linear. Some numerical examples are given to show the effectiveness.
Secondly, we have applied the first method of Lyapunov to analyze CNN’s stability when the interaction between cells is nonlinear. Another novel criterion for the global asymptotic stability of cellular neural networks has been adopted with eigen-values analysis for Lyapunov’s linear-matrix, it is feasible by experiment test.
Thirdly, a 5-order CNN hyper-chaotic system is designed according to the criterions put forward above, and it is applied to secure communication.
Fourthly, we have constructed CNN chaotic and hyper-chaotic secure communication system based on the theories for chaos synchronization and state observer, a new technical requirement has been proposed: if the state values of CNN can be arbitrarily controlled within a certain control-range, the secure communication can be realized precisely.
引文
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[2] J. Von. Neumann. Theory of Self-Reproducing Automata, edited and completed by A.W.Burks[J]. The Quarterly Review of Biology, 1967, 42(4): 521~523
[3] L. O. Chua, T. ROSKA. Cellular neural networks: Foundations and Primer[M]. Lectuer Note For the course EE129 at U.C.Berkeley, 1998,8
[4] L. O. Chua, L. Yang. Cellular neural network: Theory[J]. IEEE Trans. on. CAS, 1988, (35): 1257~1272
[5] L. O. Chua, L. Yang. Cellular neural network: Applications[J]. IEEE Transactions on Circuits System, 1988, 35(10): 1273~1290
[6]王宏霞,虞厥邦. CNN平衡点的稳定性分析[J].物理学报, 2001,12(50): 2303~2306
[7]周冬明. CNN的非线性动力学机制及应用研究[D].复旦大学, 2004
[8]雷国伟,郭东辉.基于CNN二值图像处理的欧拉数计算[J].哈尔滨工程大学学报, 2006,27(7): 202~204
[9]刘玉明,周冬明,赵东风.基于CNN超混沌特性的图像加密[J].云南大学学报, 2007,29(4): 355~35
[10]蔡欢,闵乐泉.三个态变量CNN理论及其在色盲辨色中的应用[J].中国体视学与图像分析, 2006,11(1): 27~31
[11]翁贻方,鞠磊,王坚. CNN生物视觉信息处理模型[J].北京工商大学学报, 2007,25(1): 42~47
[12]吴忠强,谭拂晓,王绍仙.基于无源化的CNN超混沌系统同步[J].物理学报, 2006,55(4): 1651~1658
[13] L. O. Chua, T. ROSKA. Cellular neural networks and Visual Computing~ Foundations and Applications[M]. Cambridge University Press, 2001
[14] T. ROSKA, V. A. Rodriguez. Towards the Visual Microprcessor:VLSI Design and the Use of Cellular Network Universal Machines[M]. John Wiley & Sons, 2000
[15] Radu Dogaru. Universality and Emergent Computation in Cellular Neural Networks, World Scientific Seriers on Nonlinear Science[M]. Imperial College Press, 2002
[16] Tao Yang. Cellular Image Processing[M]. Nova Science Publishers,Inc. 2001
[17] Matin Hanggi, George S.Moschytz. Cellular Neural Networks:Analysis,Design and Optimization[M]. Kluwer Acedemic Publishers Pub, 2000
[18]赵辽英.混沌系统同步及其在保密通信中的应用研究[D].浙江大学, 2004
[19]李永胜,张举兵,陈志辉.基于CNN技术的灰度视频交通图像边缘检测[J].交通与计算机, 2004,23(4): 28~31
[20]鞠磊,郑德玲,张蕾.基于差值控制CNN图像滤波器[J].北京科技大学学报, 2005,27(3): 375~379
[21]姚力,刘佳敏,谢咏奎等.基于CNN的图像分割及其在医学图像中的应用[J].中国科学(E辑), 2001,31: 167~171
[22] I. Aizenberg, N. Aizenberg, J. Hiltner et al. Cellular neural networks and computational intelligence in medical image processing[J]. Image Vision Computing, 2001,19: 177~18
[23] A. Paolo, B. Adriano, B. Maide et al. Image processing for medical diagnosis using CNN[J]. Nuclear Instruments and Methods in Physics Research A, 2003,497: 174~178
[24]蒋文艳,胡桂明,曾敏.一种基于CNN的视频运动对象分割的研究[J].计算机与现代化, 2007,(5):95~97
[25]周维达,汪亚明,许建龙.基于像素统计特性及CNN的运动目标分割[J].浙江理工大学学报, 2006,23(1): 39~42
[26]周维达,汪亚明,曹丽等.基于CNN和MRF的运动目标分割[J].计算机仿真, 2007,24(7): 198~201
[27] Lequan Min, zhigang Jian, Jingtao Wang. New templates CNN for processing gray-scal image with disturbed convex objects[J]. Journal of GuangXi normal university, 2002,20(1): 56~60
[28]黄蕾,刘文波.基于CNN的灰度图像边缘提取算法中模板参数的研究[J].计算机与现代化, 2006,(6): 69~73
[29]廖晓昕.细胞神网络的数学理论(I)[J].中国科学(A辑), 1994,24(9): 902~910
[30]廖晓昕. CNN的数学理论(II)[J].中国科学(A辑), 1994,24(10): 1037~1046
[31]李雪梅. CNN的稳定性: [D].湖南大学, 2002
[32] Junwei Lu , Yiqian Guo , Shengyuan Xu. Global asymptotic stability analysis for cellular neural networks with time delays[J]. Chaos, Solitons & Fractals, 2006, 29(2): 349~353
[33] J. H. Park. An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays[J]. Chaos, Solitons & Fractals, 2007, 33(2): 800~807
[34]陈新,周亮,陈运.信息论与编码[M].北京电子工业出版社, 2002,8
[35] Qiang Zhang , Xiaopeng Wei, Jin Xu. Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays[J]. Chaos, Solitons & Fractals, 2005, 23(4): 1363~9
[36]李必文,万素梅.具变时滞的CNN的周期解[J].数学杂志, 2007,27(4): 483~489
[37] Bingwen Liu, Lihong Huang. Existence and exponential stability of almost periodic solutions for cellular neural networks with mixed delays[J]. Chaos, Solitons & Fractals, 2007, 32: 95~103
[38]张安彩,冯国涛.变时滞高阶CNN周期解的存在性及其全局指数稳定性[J].湖南文理学院学报, 2007,19(2): 20~24
[39]王宏霞.混沌技术在现代保密通信中的应用研究[D].电子科技大学, 2002
[40] K. Aihara, T. Takabe, M. Toyoda. Chaotic neural network[J]. Physics Letters A, 1990,144(7): 333~340
[41]刘年生,郭东辉,吴伯僖.混沌神经网络及其在保密通信中的应用[J].电讯技术, 2002,(5): 141~147
[42]汪海明,郭仕德,赵建业等. CNN在通信信号处理中的研究进展[J].电讯技术, 2003,(2): 1~5
[43]赵建业,陈洪涛,余道衡.用CNN实现盲均衡的一种新方法[J].电子科学学刊, 2000,22(3): 423~428
[44]但渭林. CNN在通信信号处理中的应用[J].江西理工大学学报, 2006,27(4): 19~21
[45]汪海明,赵建业,郭仕德等. CNN混沌扩频通信系统的性能研究[J].电讯技术,2002,42(6): 99~103
[46]汪海明,郭仕德,赵建业等.一种用于扩频通信系统的CNN多值随机码的研究[J].电子与信息学报, 2003,25(7): 931—937
[47]冯明库.混沌及混沌保密通信的探讨[J].广东技术师范学院学报, 2005,(8): 47~50
[48]张立明.人工神经网络的模型及其应用[M].复旦大学出版社, 1993,7
[49] L.O.Chua. CNN:A Paradigm for Complexity[J]. New York:Princeton Hall Press, 1998
[50] Haiming Wang, Chengqi Cheng, Daoheng Yu. Cellular neural network approach of a class of communication probems[A]. The 7th Annual Joint Workshops on Modern Electronic Technology and Applications[C].Novermber 13~16,2002
[51] Xiaoxin Liao, Xinyu Wu, Waikai Chen.On Stability Of Celullar Neural Networks (II)[J].南京邮电学院学报, 1995,15(1): 12~19
[52]蒋大明,戴胜华.自动控制原理[M].清华大学出版社, 2003,12
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