无简并高维超混沌系统及其应用研究

Hyperchaotic system is a hot research topic in the field of chaos theory. In recent years, the design and analysis of 4 and 5-dimensional hyperchaotic chaotic systems were studied deep and successfully using the method of state feedback control. However, when the dimension is further increased, the limitations of the exiting control methods emerge, which mainly include three aspects: (1) how to allocate the positive Lyapunov exponents without degeneration and their numbers reach the possible maximum; (2) how to let the positive Lyapunov exponent values large enough allocated and the chaotic orbit can be kept globally bounded at the same time. (3) How to design chaotic encryption algorithm with higher safety performances by using higher-dimensional hyperchaotic chaotic system? This project aims to analyze the allocation mechanism of positive Lyapunov exponents with QR orthogonal decomposition methods. Using anti-control theories of chaos, we control asymptotically stable nominal system with a uniformly bounded controller. We will convert allocation of positive Lyapunov exponents to the closed pole assignment of controlled system. Combining nominal matrix design and similarity transform, adjusting parameters and positions of controller, and so on, we will construct non-degenerated higher-dimensional hyperchaotic systems. This provides a new solution approach to the above-mentioned key problems. We will design new chaotic encryption algorithms by using non-degenerated higher-dimensional hyperchaotic systems, and improve the security performances, by combining with nonlinear nominal matrix, closed-loop feedback and multiple rounds of encryption, and reducing chaos information leakage, and so on. The expected result of this project owns important theoretical significance and practical merits for improving and extending the framework of chaos theories and its applications.

超混沌系统是混沌领域的热点课题。人们基于状态反馈控制等方法，对4维和5维超混沌系统进行过深入研究并获得成功。但随着维数拓展，现有方法局限性随之凸显，其中关键问题体现在：(1) 如何配置无简并的正李氏指数，个数达到可能最大数？(2) 如何获得足够大的正李氏指数并保证轨道全局有界？(3) 如何用高维超混沌系统设计安全性更高的混沌加密算法？本项目基于QR正交分解，分析李氏指数配置机理；根据反控制原理，用一致有界控制器对渐近稳定标称系统实施反控制，将正李氏指数配置转化为受控系统闭环极点配置；结合标称矩阵设计和相似变换、控制器参数调控和位置控制等方法构造无简并高维超混沌系统，为解决上述问题提供新途径；用无简并高维超混沌系统设计混沌加密新算法，结合非线性标称矩阵、闭环反馈和多轮加密、减小混沌信息泄漏等方法增强安全性能。无简并高维超混沌系统研究对完善和拓展混沌理论框架及其应用具有重要理论意义和实用价值。

本项目针对无简并高维超混沌系统及其应用进行了深入研究，对于完善和拓展混沌理论框架及其应用具有重要理论意义和实用价值。主要研究内容包括无简并高维连续时间超混沌系统、无简并高维离散时间超混沌系统、基于无简并高维离散时间超混沌系统的混沌流密码分析与设计、基于无简并高维离散时间超混沌系统的混沌流密码的硬件实现与混沌保密通信、混沌密码的安全分析。重要结果包括：(1) 采用平均特征值准则构造无简并高维连续时间超混沌系统；(2) 无简并高维离散时间超混沌系统设计及其在视频混沌保密通信中的应用与FPGA硬件实现；(3) 自同步混沌流密码的安全分析与设计；(4) 基于多核多线程与H.264编码的视频混沌加密方案；(5) 基于Virtex-7高端FPGA硬件平台的视频混沌保密通信；(6) 组播多用户语音混沌保密通信及其ARM硬件实现；(7) 若干混沌密码的安全分析。在本项目资助下所取得的成果包括：在 IEEE Transactions、IJBC、物理学报等国内外期刊上发表标注有本基金资助号61671161的SCI收录论文17篇，出版学术专著2部，授权国家发明专利9项。