Fractional L¨¹ System Synchronization Control Of Its Confidential Communication

Due to its complex characteristics, such as extreme sensitivity to initial conditions and system parameters, continuous broadband spectrum, ergodicity, boundedness, inherent randomness, fractal dimension, universality, and statistical characteristics, chaos has been studied extensively, especially its relevant characteristics have great application values in secure communications. In recent years, with continuous renovation on the chaos synchronization methods, chaotic systems have been applied in many disciplines and become a major research focus of the nonlinear disciplines. Compared to the integer order chaotic systems, fractional ones have more complex dynamic characteristics and can better hide information in confidential communications. Therefore, the study of the fractional-order chaotic systems has greater application value.In this thesis, four methods on synchronization control of the fractional Lu system and their application in secure communications were studied with theoretical analysis and numerical simulation. The main contributions are as follows:1. Studied the fractional Lu system of adaptive hybrid projective synchronization with unknown parameters. A suitable controller with the identification of unknown parameters was proposed. The tracking control and adaptive hybrid projective synchronization of same structure Lu-Lu systems and different structure Lu-Lorenz systems were realized.2. Studied the projective synchronization of fractional order Lu system based on the state feedback control method. If the feedback gain parameters satisfies μ>0,μ2>c,μ3>-b, then two different chaotic systems can be synchronized with the state feedback controller. The same structure Lu-Lu systems and the different structure Lu-Lorenz systems can be projective synchronized with this method.3. Studied the full state projective synchronization of fractional order Lu system. The corresponding controllers were proposed to achieve full state projective synchronization of same structure Lu-Lu systems and different structure Lu-Rossler systems, respectively. 4. Studied the modified projective synchronization of the fractional Lu system. By designing an appropriate system control rate, the modified projective synchronization between the drive system and the response system can be achieved. This method was applied to the fractional Lii system chaotic masking secure communication. Numerical simulations showed the effectiveness of this schema.