复动力系统的混沌控制与同步及其在通信中的应用

发布时间：2018-03-17 19:37

本文选题：复动力系统　切入点：混沌控制　出处：《山东大学》2014年博士论文　论文类型：学位论文

【摘要】：目前,复动力系统己广泛地应用到通信、金融、生物等多个学科中.复混沌系统就是一个典型的复动力系统.自从1982年复Lorenz方程被提出以来,复混沌系统在物理学的许多领域发挥了重要作用,尤其是通信系统.复变量增加了所传输信息的内容并提高了安全性.复混沌系统的控制和同步成为混沌保密通信的热点问题.因此,本文对复混沌系统的控制和同步及其在安全通信中的应用进行了一系列基础研究,其主要工作和创新点如下： 1.实混沌系统的控制与同步对于连续系统,提出了累积误差控制器.该控制器采用了累积误差的线性函数,在实际工程上可由RC电路实现.对于离散系统,提出了误差反馈矩阵控制.它类似于线性系统的状态反馈,但是该矩阵是时变的,包含状态变量的耦合信息,根据梯度下降法在线更新,并趋于一个恒定矩阵.结合变量间的耦合关系,本文还提出了部分矩阵控制和全矩阵控制.部分矩阵控制仅采用对部分变量的控制就实现全部变量达到期望值,易于工程实现.但是,上述控制器只能实现不动点控制和自同步.因此,结合速度梯度法和非线性函数控制,本文实现了带有未知参数的连续混沌系统的跟踪任意有界参考信号和参数辨识. 2.复混沌系统的复比例因子投影同步与参数辨识提出了复比例因子投影同步(CMPS).完全同步(CS),反同步(AS),投影同步(PS)和修正投影同步(MPS)都是CMPS的特殊情况,因此它包含了以前的工作并进行推广.考虑到复混沌系统的未知参数和有界干扰的各种可能情形,本文设计了带有收敛因子和动态控制力量CMPS控制器；同时基于可持续激励和线性独立给出了参数收敛到真值的充分条件和必要条件,给出了改变比例因子的方法以辨识出参数真值.另外,CMPS在实混沌系统和复混沌系统之间建立同步联接.因此,本文首次讨论了实混沌系统和复混沌系统的复比例因子投影同步,基于速度梯度法设计了包含伪梯度条件的同步控制器. 3.复混沌系统的复函数同步及其通信方案提出复函数投影同步(CFPS). CS, AS, PS, MPS,全状态组合投影同步(FSHPS),函数投影同步(FPS),修正函数投影同步(MFPS),广义函数投影同步(GFPS)和CMPS都是CFPS的特殊情形.CFPS几乎没有被研究过,而且将包括大部分存在的同步情形.针对带有未知参数的复混沌系统,设计了CFPS控制器,并针对耦合复混沌系统,设计了基于CFPS的通信方案.该通信方案本质上是混沌掩盖,但是所传输的信号是信息信号(作为复比例函数)与混沌信号积的导数.因为复比例函数比实函数更加不可预测和复杂,则入侵者从传输信号中提取信息的可能性更小. 4.复混沌系统的差函数投影同步及其通信方案从两复函数相减的角度提出了差函数投影同步(DFPS),自同步和相位同步均是其特殊情形.设计了DFPS控制器,并将其应用到耦合复混沌系统中,提出了基于DFPS的通信方案.该通信方案本质上仍是混沌掩盖,但是所传输的信号是信息信号和混沌信号的和的导数.它避免了CFPS中由于驱动系统状态(作为除数)接近零时产生的算法误差. 5.时滞复混沌系统的自时滞同步及其通信方案提出了复混沌系统的自时滞同步(STDS),它是自同步的扩展,进一步拓宽了同步问题的视野,并避免了因时滞而产生的各种问题.时滞复混沌系统能产生高度随机性和不可预测性的时间序列,应用在混沌保密通信中能够提高保密性能.因此,本文研究了时滞复Lorenz系统的混沌特性,并设计控制器实现了时滞复Lorenz系统的自时滞同步.针对耦合时滞复混沌系统,给出了基于STDS的通信方案.该通信方案考虑了信息传输中产生的时滞,更接近实际情况,时滞复混沌系统也进一步增强了保密效果. 综上所述,本文围绕复动力系统的混沌控制与同步及其在通信中的应用展开了研究,提出了复比例因子投影同步,复函数投影同步,差函数投影同步及自时滞同步等概念,并将复变量引入到混沌通信中,促进了复动力系统的发展,为进一步加强通信安全提供了理论依据.
[Abstract]:At present, the complex dynamic system has been widely applied to communications, finance, biology and other disciplines. More complex chaotic system is a typical complex dynamic system. Since 1982 the complex Lorenz equation is proposed, the chaotic system has played an important role in many areas of physics, especially the complex variable increase communication system. The transmission of information content and improve security. The complex control and synchronization of the chaotic systems has become a hot issue of chaotic secure communication. Therefore, the control of complex chaotic system and synchronization and its application in secure communication of a series of basic research, the main work and innovation are as follows:
Control and synchronization of 1. real chaotic systems
For the continuous system, put forward the cumulative error controller. The controller uses a linear function of accumulated error in practical engineering can be realized by the RC circuit. For the discrete system, put forward the error feedback control matrix. It is similar to the linear system state feedback, but the matrix is time-varying, contains the coupling information of state variables according to the gradient descent method, online updates, and tends to be a constant matrix. Combined with the coupling relationship between the variables, this paper also put forward the part matrix control and full matrix control. Some matrix control using only part of the control variables on all variables reached expectations, easy to realize. However, the controller can only control and self synchronization of the fixed point. Therefore, combined with the velocity gradient method and nonlinear control function, this paper realizes continuous chaotic system with unknown parameters tracking arbitrary bounded reference letter Number and parameter identification.
Complex proportional factor projection synchronization and parameter identification of 2. complex chaotic systems
The complex scaling factor of projective synchronization (CMPS) (CS). The complete synchronization, anti synchronization, projective synchronization (AS) (PS) and modified projective synchronization (MPS) is a special case of CMPS, so it contains the previous work and promotion. Considering the unknown parameters of chaotic systems and complex all the possible interference, this paper designed a convergence factor and dynamic power control CMPS controller; at the same time, sustainable motivation and linear independence parameters converge to the true value of the sufficient conditions and necessary conditions are given based on the proposed change scale factor to identify the true value of the parameters. In addition, the establishment of synchronous connection between CMPS chaotic systems and complex chaotic system. Therefore, this paper first discusses the complex chaotic systems and complex real projective synchronization of chaotic systems, based on the velocity gradient method to design the synchronization controller contains pseudo gradient conditions.
Complex function synchronization of 3. complex chaotic systems and its communication scheme
The complex function projective synchronization (CFPS). CS, AS, PS, MPS, a combination of full state projective synchronization (FSHPS), function projective synchronization (FPS), modified function projective synchronization (MFPS), the generalized function projective synchronization (GFPS) and CMPS CFPS are the special cases of.CFPS have been little studied, and most will include synchronization scenarios exist. For complex chaotic systems with unknown parameters, a CFPS controller is designed, and the complex coupled chaotic systems, designs the communication scheme based on CFPS. The communication scheme is essentially chaotic signal, but the transmission of information signals (as complex function) derivative and chaos signal product. Because the more unpredictable than real function and complex complex function, is less likely to extract information from the signal transmission.
Differential projection synchronization and communication scheme for 4. complex chaotic systems
From the two points of complex function subtraction difference function projective synchronization (DFPS), self synchronization and phase synchronization are its special cases. DFPS controller is designed, and its application to complex coupled chaotic systems, proposes a communication scheme based on DFPS. The communication scheme is essentially chaotic, but signal transmission is a derivative information signal and chaotic signal. And it avoids CFPS due to driving system state (as close to zero divisor) algorithm error generated.
Self time delay synchronization and communication scheme for 5. time delay complex chaotic systems
The complex chaotic system of self synchronization of time delay (STDS), it is a self synchronous expansion, to further expand the synchronization problem of vision, and to avoid the problems caused by time delay. Delay complex chaotic system can produce highly random and unpredictable time series should be used, can improve the security performance in the chaotic secure communication. Therefore, the chaotic characteristics are studied in this paper with complex Lorenz system, self synchronization of time delay and time delay controller is designed to realize the complex Lorenz system. Aiming at the complex chaotic system coupling delay, gives the communication scheme based on STDS. The communication scheme considering the delay of information transmission, closer to the actual situation. Complex chaotic systems with time delay but also further enhance the security effect.
To sum up, this paper focuses on the complex dynamic system synchronization control and its application in communication research, the complex scaling factor of projective synchronization, synchronization of complex function projection difference function projective synchronization and self synchronization of time delay concepts and complex variables into chaotic communication, promote the development of complex dynamic system. To provide a theoretical basis for further strengthening the communication security.

【学位授予单位】：山东大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN918;O415.5

【参考文献】