【作者】 魏强；

【导师】 胡小鹏；

【作者基本信息】 大连理工大学 ， 计算机应用技术， 2015， 博士

【摘要】 复杂系统的混沌控制和同步方法的研究是非线性科学研究的热点问题之一。目前,对复杂系统中的实／复单系统的混沌控制以及同步方法已经取得了大量研究成果。但是对单混沌系统混沌控制的控制器设计往往是比较复杂、多维、步骤繁琐且计算量较大。对单系统同步的研究多为有限时间的完全同步。为此,本文对复杂系统中的单系统的混沌控制、复系统的同步及复杂动态网络的同步做了较深入的研究。本文的主要创新点如下：(1)对实系统的混沌控制做了较为深入的研究。提出了混沌永磁同步电机的逆最优控制方法；根据逆最优控制方法及Lyapunov稳定性理论证明了该控制器的可有效性。又提出了基于三角形稳定理论及混合投影同步的有限时间混沌控制方法,该方法步骤简单实施容易,可有效的实现有限时间混沌控制。在此研究的基础上,提出了LMI(Linear Matrix Inequality)模糊有限时间混沌控制方法；根据有限时间稳定理论及Lyapunov稳定理论证明了有限时间控制器可在有限时间内实现混沌控制。仿真实验进一步验证了上述方案的正确性。(2)对有限时间投影同步做了进一步的研究。在提出的有限时间统一混沌系统的混合投影同步的基础之上,又提出了有限时间统一混沌系统的混合函数投影同步。根据有限时间稳定理论及Lyapunov稳定理论,设计出有限时间控制器,理论证明了统一混沌系统可在有限时间内实现混合／函数投影同步。仿真实验进一步验证了上述两种方案的正确性。(3)对复系统及复杂动态网络同步做了较为深入的研究。提出了复系统的混合复函数投影同步方法,以及具有复扰动的复系统同步方法。根据Lyapunov稳定性理论,采用反馈控制方法,设计了自适应复数反馈控制器。理论证明了控制器可使复系统的同步误差渐进的趋向于零点。最后,提出了复杂网络的自适应混合函数投影同步方法,根据Lyapunov稳定性理论,采用反馈控制方法,设计了反馈控制器,理论证明了控制器可以使混合函数投影同步误差渐进的趋向于零点。仿真实验进一步验证上述方案的正确性。更多还原

【Abstract】 Research on chaotic control and synchronization method of complex nonlinear system is one of the hot issues of nonlinear science. At present, the chaotic control and synchronization method of the real/complex single system in complex nonlinear system and complex networks has made a lot of research results. However, the controller design of chaotic single system is multidimensional, step complicated and large amount of calculation. The study of single system synchronization are all finite time completely synchronization. Therefore, in this paper, the further research on the chaos control and synchronization of single system, synchronization of complex system.In this thesis, our main work is as follows:(1) Further research on the chaotic control of real variable chaotic system, puts forward the inverse optimal control method for controlling chaos of the permanent magnet synchronous motor. According to inverse optimal control method and Lyapunov stability theory proves that the correctness of controller. And puts forward the problem of finite time control for the unified chaotic system base on triangle stability theory and hybrid projection synchronized methods, procedures simple implementation easy and can effectively realize the finite time chaos control. With the support of the study above, put forward LMI fuzzy finite-time control. According to the theory of finite time stable and Lyapunov theory of stable proves the finite time controllers can achieve chaos control in a finite time. Simulation results further validate the above correctness of the schemes.(2) Further research on finite time projective synchronization, put forward the method of hybrid projective synchronization and function projective synchronization for the unified chaotic systems. Based on the Lyapunov stability theory and the theory of finite time stable, the finite time controllers are designed, which can make chaotic unified chaotic systems realize hybrid/function projective synchronization. The numerical simulation further verifies the above correctness of the schemes.(3) Further research on the synchronization of the complex system and complex network, put forward the hybrid complex (function) protective synchronization of the complex system, and synchronization of the complex system with disturbance. According to the theory of Lyapunov stability, feedback controllers are designed by the adaptive method. The theory proves that the above two kinds of controller can make the synchronization error of the complex system gradually tends to zero. Finally, put forward adaptive hybrid function projective synchronization of the complex network, the feedback controller is designed base on Lyapunov stability theory, the theory proves that the controller can make the mixed function projective synchronization error gradually tends to zero. The numerical simulation further verifies the correctness of the schemes.更多还原