混沌修正函数投影同步控制与应用研究
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摘要
混沌修正函数投影同步是近几年刚刚发展起来的一种新型同步方式。其实现同步的同步尺度因子是一个函数矩阵，而不是常量，这意味着驱动系统和响应系统能按照一定的函数比例关系进行同步，这种特性对加强数字保密通信的安全性具有重要意义。本论文针对具有模型不确定和外界干扰的混沌系统，研究了各种条件下实现修正函数投影同步的控制策略，并将其应用于保密通信，其主要研究研究工作和创新点如下：
将函数投影同步与降阶同步相结合，提出了降阶修正函数投影同步的概念，并将修正函数投影同步的函数尺度因子矩阵由给定的可微函数拓展到在相空间中具有平衡点、周期轨道、混沌状态的混沌吸引子。基于Lyapunov稳定性理论和状态反馈控制方法，给出了具有参数扰动的同阶混沌系统修正函数投影同步和不同阶混沌系统降阶修正函数投影同步的一般方法。
针对具有模型不确定和外界扰动的混沌驱动系统，利用单向耦合混沌同步原理，给出了两种响应系统的设计方案，并设计了控制器和自适应律，实现了混沌驱动—响应系统的修正函数投影同步。其中耦合反馈系数可随自适应律自由调整到最佳值，不需要设计者进行调试。
设计了统一的鲁棒自适应滑模控制器，实现了具有不确定参数、模型不确定和外界扰动的同结构和异结构混沌系统的修正函数投影同步。进一步考虑了实际系统中控制输入的非线性，讨论了具有已知和未知扇区非线性输入、模型不确定和外界扰动的混沌系统的修正函数投影同步问题。以典型混沌系统为例的理论分析和仿真结果表明该方法的有效性。
基于产生超混沌系统要满足的两个必要条件构建了一个新的四维超混沌系统并将其命名为Fang超混沌系统，通过对其基本动力学特性的分析验证了该系统的混沌行为。将错位同步与函数投影同步相结合，提出了一种新的概念—错位修正混沌函数投影同步。基于Lyapunov稳定性定理和主动控制方法，设计鲁棒自适应控制器和参数更新规则，实现了受扰Fang超混沌系统的错位修正函数投影同步。
将混沌修正函数投影同步应用于保密通信中。第一种方案是将混沌修正函数投影同步和参数调制相结合。第二种方案是将耦合修正函数投影同步和混沌遮掩相结合。以新构造的Fang超混沌系统为例的数值仿真证明了上述保密通信方案的有效性。
Modified function projective synchronization is a new type of synchronization method developedin recent years. The scale factor of modified function projective synchronization is a function, ratherthan a constant,which means that the drive and response system could be synchronized up to a desiredscaling function matrix. This feature can strengthen the security of digital securecommunication. This thesis focuses on the design of chaotic synchronization controller of chaoticsystems with model uncertainties and external disturbances under various conditions, and itsapplication in the secure communication.The main works and innovative points of this paper are asfollows:
The concept of reduced-order modified function projective synchronization of chaotic systems isproposed.The given scaling function can be an equilibrium point, a periodic orbit, or even a chaoticattractor in the phase space.Based on Lyapunov stability theory and state feedback control method,thegeneral control methods are given,by which one can realize the modified function projectivesynchronization of chaotic system with same order and the reduced-order modified functionprojective synchronization of chaotic system with different order.
A general method of modified function projective synchronization of a class of chaotic systemswith model uncertainties and external perturbation is proposed by designing a suitable responsesystem．Based on unidirectional coupled synchronization,the two schemes of obtaining the responsesystem from chaotic drive system are established. By designing suitable controller and adaptivelaw,the drive and response systems can synchronize to a desired scaling function matrix.The couplingstrength can be automatically adapted to a updated law.
A general robust adaptive sliding mode controller is designed to realize the modified functionprojective synchronization of two same-structure chaos system and different-structure chaossystem,which have parameters mismatch、model uncertainities and external disturbances. On thebasis of the previous chapters, the nonlinear control input in the actual system is further considered.The modified function projective synchronization of chaotic system with known or unknown sectornonlinearity input、model uncertainties and external perturbation is discussed. Simulation results ofthe typical chaotic system show the effectiveness of the proposed controller.
A new four dimensional continuous time autonomous hyperchaotic system named Fanghyperchaotic system is proposed in this paper,which is built by the two necessary conditions of hyperchaotic system. The hyperchaotic system is analyzed by studying the basic dynamiccharacteristics. The concept of dislocated modified function projective synchronization of chaoticsystems is proposed. Based on Lyapunove stability theory and active control method,a robust adaptivefeedback controller is presented for the dislocated modified function projective synchronization ofFang hyperchaotic system.
The modified function projective synchronization method is applied to secure communication.One method is based on the modified function projective synchronization and parameter modulate,theother method is based on the coupled modified function projective synchronization and chaoticmask.The corresponding numerical simulations of Fang hyperchaotic system demonstrate theeffectiveness of the proposed methods.
将函数投影同步与降阶同步相结合，提出了降阶修正函数投影同步的概念，并将修正函数投影同步的函数尺度因子矩阵由给定的可微函数拓展到在相空间中具有平衡点、周期轨道、混沌状态的混沌吸引子。基于Lyapunov稳定性理论和状态反馈控制方法，给出了具有参数扰动的同阶混沌系统修正函数投影同步和不同阶混沌系统降阶修正函数投影同步的一般方法。
针对具有模型不确定和外界扰动的混沌驱动系统，利用单向耦合混沌同步原理，给出了两种响应系统的设计方案，并设计了控制器和自适应律，实现了混沌驱动—响应系统的修正函数投影同步。其中耦合反馈系数可随自适应律自由调整到最佳值，不需要设计者进行调试。
设计了统一的鲁棒自适应滑模控制器，实现了具有不确定参数、模型不确定和外界扰动的同结构和异结构混沌系统的修正函数投影同步。进一步考虑了实际系统中控制输入的非线性，讨论了具有已知和未知扇区非线性输入、模型不确定和外界扰动的混沌系统的修正函数投影同步问题。以典型混沌系统为例的理论分析和仿真结果表明该方法的有效性。
基于产生超混沌系统要满足的两个必要条件构建了一个新的四维超混沌系统并将其命名为Fang超混沌系统，通过对其基本动力学特性的分析验证了该系统的混沌行为。将错位同步与函数投影同步相结合，提出了一种新的概念—错位修正混沌函数投影同步。基于Lyapunov稳定性定理和主动控制方法，设计鲁棒自适应控制器和参数更新规则，实现了受扰Fang超混沌系统的错位修正函数投影同步。
将混沌修正函数投影同步应用于保密通信中。第一种方案是将混沌修正函数投影同步和参数调制相结合。第二种方案是将耦合修正函数投影同步和混沌遮掩相结合。以新构造的Fang超混沌系统为例的数值仿真证明了上述保密通信方案的有效性。
Modified function projective synchronization is a new type of synchronization method developedin recent years. The scale factor of modified function projective synchronization is a function, ratherthan a constant,which means that the drive and response system could be synchronized up to a desiredscaling function matrix. This feature can strengthen the security of digital securecommunication. This thesis focuses on the design of chaotic synchronization controller of chaoticsystems with model uncertainties and external disturbances under various conditions, and itsapplication in the secure communication.The main works and innovative points of this paper are asfollows:
The concept of reduced-order modified function projective synchronization of chaotic systems isproposed.The given scaling function can be an equilibrium point, a periodic orbit, or even a chaoticattractor in the phase space.Based on Lyapunov stability theory and state feedback control method,thegeneral control methods are given,by which one can realize the modified function projectivesynchronization of chaotic system with same order and the reduced-order modified functionprojective synchronization of chaotic system with different order.
A general method of modified function projective synchronization of a class of chaotic systemswith model uncertainties and external perturbation is proposed by designing a suitable responsesystem．Based on unidirectional coupled synchronization,the two schemes of obtaining the responsesystem from chaotic drive system are established. By designing suitable controller and adaptivelaw,the drive and response systems can synchronize to a desired scaling function matrix.The couplingstrength can be automatically adapted to a updated law.
A general robust adaptive sliding mode controller is designed to realize the modified functionprojective synchronization of two same-structure chaos system and different-structure chaossystem,which have parameters mismatch、model uncertainities and external disturbances. On thebasis of the previous chapters, the nonlinear control input in the actual system is further considered.The modified function projective synchronization of chaotic system with known or unknown sectornonlinearity input、model uncertainties and external perturbation is discussed. Simulation results ofthe typical chaotic system show the effectiveness of the proposed controller.
A new four dimensional continuous time autonomous hyperchaotic system named Fanghyperchaotic system is proposed in this paper,which is built by the two necessary conditions of hyperchaotic system. The hyperchaotic system is analyzed by studying the basic dynamiccharacteristics. The concept of dislocated modified function projective synchronization of chaoticsystems is proposed. Based on Lyapunove stability theory and active control method,a robust adaptivefeedback controller is presented for the dislocated modified function projective synchronization ofFang hyperchaotic system.
The modified function projective synchronization method is applied to secure communication.One method is based on the modified function projective synchronization and parameter modulate,theother method is based on the coupled modified function projective synchronization and chaoticmask.The corresponding numerical simulations of Fang hyperchaotic system demonstrate theeffectiveness of the proposed methods.
引文
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