典型分数阶混沌系统若干同步方法分析-控制科学与工程专业论文.docxVIP

重庆大 重庆大学硕士学位论文 英文摘要 PAGE PAGE III ABSTRACT Chaos universally exists in natural sciences and social sciences, which is a special nonlinear system. In recent years, chaos has attracted attentions of many scholars in mathematics and control. The research of chaos has been studied deeply. Chaotic systems are sensitive to the initial conditions and can not be predictied. Thus it will be widely used in many fields, especially in the security of communication. This paper puts emphasis on studying the approach of synchronizing fractional-order chaotic system. As the stable theory for fractional-order chaotic systems is a developing area and less perfect than the stable theory for integer-order chaotic systems， it hinders the development of the synchronizing and controlling approach of fractional-order chaotic systems. The main contribution of this thesis is about fractional-order systems as follows: ① In view of chaos synchronization of a class of fractional-order chaotic systems, a novel adaptive controller and adaptive updating law are designed based on the quasi-Lyapunov stability theory for fractional-order systems. Compared with the existing results, the derived method has some advantages such as simple structure, low control cost and high generality. Furthermore, the method can apply to most typical fractional-order chaotic systems. ② This thesis investigates the synchronization of fractional-order chaotic systems via sliding mode control method. A fractional-order sliding surface is proposed and the corresponding controller is formulated based on the fractional version of the Lyapunov stability theory, which can guarantees asymptotical stability of fractional-order chaotic systems. On this basis, A fractional-order sliding surface is proposed and the corresponding controller with the adaptive laws is formulated. ③ In view of chaos synchronization of fractional-order chaotic systems, a method which can convert the fractional-order synchronization problem into an eq