混沌系统的同步及其在保密通信中的应用
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摘要
混沌运动是一种非常有趣的非线性现象,在过去的三十年当中,对于混沌的研究逐步深入,在很多物理系统中如电子、机械、热力学系统等都检测到了混沌现象的存在。
混沌运动是一种确定性的非线性运动,它的运动轨迹非常复杂但又不完全随机。由于混沌信号的遍历性、非周期、连续宽带动态频谱等特性对保密通信非常有利体现出混沌理论在保密通信方面潜在的应用价值,所以混沌控制与同步已经成为混沌科学一个非常重要的研究课题。
本文以连续混沌系统为研究对象,主要内容包括动态混沌系统的同步分析,以及混沌同步在通信方面的应用,同时也阐述了几种混沌同步的方法。
首先介绍了混沌同步理论应用于保密通信的几种主要方法,如混沌掩盖、混沌调制、混沌键控以及混沌扩频等方法。本文用驱动系统状态来设计加密函数,通过通道把加密函数加密的信息传输到接收机,在接收端用相应的解密函数恢复出原信号。传输中,加密函数和解密函数的使用加大了传送信号的复杂性,提高了保密通信的保密能力。
接着重点介绍了一般的把非线性系统线性化的方法,研究了把混沌系统线性化的方法,进一步探讨了线性反馈控制和非线性反馈控制下的混沌同步及在保密通信中的应用,设计出一种非线性控制器来同步两个混沌系统的输出信号并构造了保密通信系统。
同时又研究了基于非线性观测器理论的混沌同步控制方法,通过重构系统的状态,并用重构的状态来代替系统的真实状态最终实现系统要求的状态反馈。进一步介绍了线性和非线性系统的观测器设计的一般方法,而且对Lipshitz非线性系统的设计问题进行了探讨,实现了代有满足Lipshitz条件的非线性项的两个混沌系统的同步。然后用混沌调制方法构造相应的混沌保密通信系统。
最后以稳定性理论为基础,针对一类连续混沌系统,当系统状态或参数部分已知时,验证一种自适应同步控制方法并分析了这种方法理论上的可行性。在此基础之上,基于Lyapounv稳定性理论,设计一种自适应观测器来确保误差系统是渐进稳定的,从而使得两个混沌系统最终达成同步。并且通过数值仿真说明设计方法是有效的,最终以此混沌同步理论为指导构造出保密通信系统。
Chaotic behaviour is an interesting nonlinear phenomenon which has been intensively studied during the last three decades. Chaotic behaviour is commonly detected in a wide and variety of physical systems, such as electrical, mechanical and thermal systems.
Chaotic motion is a complex nonlinear motion, whose trajectory of orbits in the phase plane is very complex but not stochastic. On the other hand, the dynamic properties of chaos signal such as ergodicity, aperiodic, uncorrelated, broad band and picture encrypt systems, so chaos control and chaos synchronization has become a very important topic in chaos science due to its potential application in secure communication.
This paper discussed with the continuous-time chaotic systems as the objects. The main content contains the analysis of the synchronization of chaotic dynamical system and its application on secure communication.
First a few main message encoding methods based on chaotic synchronization have been developed:Chaotic masking, Chaos modulation and Chaos shift keying. This paper designs the encryption function with the driving system's chaotic states. Then the messages encrypted are sent to receiver with two chaotic systems synchronization. At the receiver, the decryption function associated with encryption function recovered the original messages. The utilization of encryption function and decryption function increase complexity of the transmitted signal, make a contribution to the development of secret communication.
Further chaotic synchronization based on nonlinear feedback control was researched. through theoretic proving we found that the chaotic synchronization can be obtained from the synchronization of the outputs of two systems. This paper gives a linear and nonlinear controller to synchronize two chaotic systems which was used to construct secure communication system.
At the same time, the nonlinear observer-based synchronization of chaotic systems and application in secure communication was discussed. This scheme to solve this problem is to reconstruct the state variables of the system and to use it to replace the actual state variables of the original system to satisfy the requirement of the state feedback. Furthermore, the problems related to the design of observer for Lipschitz nonlinear systems are discussed. Based on the conclusions, the problems of the design methods of observer for Lipschitz chaos systems are dealt with. The observer-based synchronization of chaos systems with nonlinear terms satisfying Lipschitz conditions is realized. The chaotic modulation has been developed for synchronized chaotic communication system.
At last, on the basis of stability theorem, this paper put forward a self-adaptive synchronization control method for a kind of continuative systems. When only partial information or parameters of the systems states are known, by Lyapounv theory, theoretic feasibility proof of the methods, self-adaptive synchronization controller are constructed, an self-adaptive observer is designed to ensure the corresponding error system asymptotically stable. A numerical example is included to show the effectiveness of the proposed techniques.
混沌运动是一种确定性的非线性运动,它的运动轨迹非常复杂但又不完全随机。由于混沌信号的遍历性、非周期、连续宽带动态频谱等特性对保密通信非常有利体现出混沌理论在保密通信方面潜在的应用价值,所以混沌控制与同步已经成为混沌科学一个非常重要的研究课题。
本文以连续混沌系统为研究对象,主要内容包括动态混沌系统的同步分析,以及混沌同步在通信方面的应用,同时也阐述了几种混沌同步的方法。
首先介绍了混沌同步理论应用于保密通信的几种主要方法,如混沌掩盖、混沌调制、混沌键控以及混沌扩频等方法。本文用驱动系统状态来设计加密函数,通过通道把加密函数加密的信息传输到接收机,在接收端用相应的解密函数恢复出原信号。传输中,加密函数和解密函数的使用加大了传送信号的复杂性,提高了保密通信的保密能力。
接着重点介绍了一般的把非线性系统线性化的方法,研究了把混沌系统线性化的方法,进一步探讨了线性反馈控制和非线性反馈控制下的混沌同步及在保密通信中的应用,设计出一种非线性控制器来同步两个混沌系统的输出信号并构造了保密通信系统。
同时又研究了基于非线性观测器理论的混沌同步控制方法,通过重构系统的状态,并用重构的状态来代替系统的真实状态最终实现系统要求的状态反馈。进一步介绍了线性和非线性系统的观测器设计的一般方法,而且对Lipshitz非线性系统的设计问题进行了探讨,实现了代有满足Lipshitz条件的非线性项的两个混沌系统的同步。然后用混沌调制方法构造相应的混沌保密通信系统。
最后以稳定性理论为基础,针对一类连续混沌系统,当系统状态或参数部分已知时,验证一种自适应同步控制方法并分析了这种方法理论上的可行性。在此基础之上,基于Lyapounv稳定性理论,设计一种自适应观测器来确保误差系统是渐进稳定的,从而使得两个混沌系统最终达成同步。并且通过数值仿真说明设计方法是有效的,最终以此混沌同步理论为指导构造出保密通信系统。
Chaotic behaviour is an interesting nonlinear phenomenon which has been intensively studied during the last three decades. Chaotic behaviour is commonly detected in a wide and variety of physical systems, such as electrical, mechanical and thermal systems.
Chaotic motion is a complex nonlinear motion, whose trajectory of orbits in the phase plane is very complex but not stochastic. On the other hand, the dynamic properties of chaos signal such as ergodicity, aperiodic, uncorrelated, broad band and picture encrypt systems, so chaos control and chaos synchronization has become a very important topic in chaos science due to its potential application in secure communication.
This paper discussed with the continuous-time chaotic systems as the objects. The main content contains the analysis of the synchronization of chaotic dynamical system and its application on secure communication.
First a few main message encoding methods based on chaotic synchronization have been developed:Chaotic masking, Chaos modulation and Chaos shift keying. This paper designs the encryption function with the driving system's chaotic states. Then the messages encrypted are sent to receiver with two chaotic systems synchronization. At the receiver, the decryption function associated with encryption function recovered the original messages. The utilization of encryption function and decryption function increase complexity of the transmitted signal, make a contribution to the development of secret communication.
Further chaotic synchronization based on nonlinear feedback control was researched. through theoretic proving we found that the chaotic synchronization can be obtained from the synchronization of the outputs of two systems. This paper gives a linear and nonlinear controller to synchronize two chaotic systems which was used to construct secure communication system.
At the same time, the nonlinear observer-based synchronization of chaotic systems and application in secure communication was discussed. This scheme to solve this problem is to reconstruct the state variables of the system and to use it to replace the actual state variables of the original system to satisfy the requirement of the state feedback. Furthermore, the problems related to the design of observer for Lipschitz nonlinear systems are discussed. Based on the conclusions, the problems of the design methods of observer for Lipschitz chaos systems are dealt with. The observer-based synchronization of chaos systems with nonlinear terms satisfying Lipschitz conditions is realized. The chaotic modulation has been developed for synchronized chaotic communication system.
At last, on the basis of stability theorem, this paper put forward a self-adaptive synchronization control method for a kind of continuative systems. When only partial information or parameters of the systems states are known, by Lyapounv theory, theoretic feasibility proof of the methods, self-adaptive synchronization controller are constructed, an self-adaptive observer is designed to ensure the corresponding error system asymptotically stable. A numerical example is included to show the effectiveness of the proposed techniques.
引文
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