一类复杂动力系统的参数辨析

对一类复杂系统(Lorenz混沌和Rssler超混沌)的未知参数提出一种简便的辨析方法.首先,通过对系统实行反馈控制使其到达任意不动点,然后,通过求解不动点的平衡方程,解析地得到系统未知参数的表达式.以Lorenz混沌为例将该方法和线性参数观测器的方法进行对比,可以更快地实现该系统全部未知参数的准确快速辨析.在系统参数发生阶跃变化的情况下,该方法可很好地实现对参数高精度的快速辨析.数值计算结果和理论分析一致.该方法可以推广到其他复杂动力系统的参数结构辨析研究.

Parameters Identification for One Class of Complex System

It gives a method of the identification for unknown parameters of one class of complex systems (Lorenz chaotic and hyper chaotic systems),by controlling them to reach desired stable point with feedback control method. It is easy to get the frondose form of observer for unknown parameters by solving the equilibrium equation when the system is led to the desired stable points. This method is more powerful and useful compared with the traditional linear observer method, because it can find all the unknown parameters altogether. The method is also effective to identify the unknown parameters of the complex systems, even if the parameters may jump or vary slowly. The numerical simulation result is consistent with the theory analysis. Therefore, the method can be used to study other complex system for parameter identification.