一类不确定分数阶混沌系统自适应同步与参数辨识

Adaptive synchronization and parameter identification of one class of uncertain fractional-order chaotic system

针对一个参数不确定的分数阶混沌系统,首先给出不同相平面上的混沌吸引子图,然后基于分数阶系统稳定性理论,设计了一种自适应同步控制方法,不仅能够实现该系统的混沌同步,同时能够完成响应系统的参数辨识,并根据Lyapunov稳定性理论给予严格证明,最后通过数值仿真,验证了该方法的有效性和正确性.

In view of one parameter uncertain fractional-order chaotic system, firstly, the chaotic attractors of different phase plane are given. Then, based on the fractional-order stability theory, suitable adaptive synchronization controllers are designed. The method not only achieves the chaos synchronization of the system, but also identifies unknown parameters of the respond system. At last based on the Lyapunov stability theory, strict mathematic proof is given, numerical simulation demonstrates the effectiveness and correctness of the method.