基于重构系统的扩张状态观测器实现混沌系统的同步

Synchronizing chaos based on the extended state observer of the reconstructed system

利用n阶驱动系统的标量输出信号及其连续的n-1阶导数作为状态变量,得到一个具有Brunowsky规范形式的n阶重构系统。根据扩张观测器的思想,对此重构系统先构造扩张系统,然后设计扩张状态观测器,并将其作为响应系统。通过挖掘可测同步误差中所隐含的信息对扩张系统的各个状态进行估计,从而实现了系统的输出及其导数的同步。当满足一定条件,还可实现所有状态变量的同步。对R&o&ssler系统、Duffing系统的仿真证明了该方法的有效性。

A n-order reconstructed system is designed in Brunowsky canonical form by using a scalar output signal of n-order driving system and its successively n-1 order derivatives to reconstruct state variables. An extended system is formed for the reconstructed system based on the extended state observer, and then an extended state observer is designed and looked as response system. Synchronizing output of chaotic system and its derivatives is realized by collecting the information wrapped in observable synchronizing error to estimate the states. When some conditions are satisfied, synchronizing all state variables is realized. Simulation results of Rossler system and Duffing system manifest the valid of this method.