异结构的分数阶超混沌系统函数投影同步及参数辨识

摘要

The function projective synchronization and parameter identification between the fractional-order chaotic system and hyper-chaotic system with uncertain parameters are researched, in which the fractional-order Chen chaotic system and the new fractional-order hyper-chaotic system are as examples. First, based on the fractional theory of stability and nonlinear dynamic theory, the nonlinear controller and parameter identification rules are designed. And by the nonlinear controller the function projective synchronization between the fractional-order 3D chaotic system and 4D hyper-chaotic system with uncertain parameters are realized. At the same time, the uncertain parameters are identified. Second, based on the fractional-order theory of stability the synchronization are proved strictly in mathematics. Finally, by the Predictor-Corrector scheme numerical simulation, the validity of the presented method is verified.%　　该文以分数阶 Chen 混沌系统和一个新的分数阶超混沌系统为例，研究参数不确定的分数阶混沌系统和超混沌系统函数投影同步及参数辨识。首先，基于分数阶系统稳定性理论和非线性动力学理论，构造出相应的非线性控制器和不确定参数的辨识规则；由此实现了参数不确定的分数阶超混沌系统的函数投影同步及不确定参数的辨识。其次，利用分数阶稳定性理论，对上述同步给出了严格的数学证明。最后，借助于预估-校正算法，利用数值模拟验证了所提方法的有效性。