基于共轭梯度法的混沌系统参数辨识和同步

Parameter identification and synchronization of chaotic system using conjugate gradient method

提出基于共轭梯度法和驱动响应同步思想的未知参数混沌系统的参数辨识和混沌同步新方法。该方法采用驱动系统的单变量驱动与其结构相同参数可调的响应系统,由于混沌对于参数的失配具有极度敏感性,参数不同的两个相同结构的混沌系统无法同步,因此通过调整响应系统参数使同步误差最小就可以实现混沌同步,同时得到驱动系统参数。本文通过共轭梯度方法搜索使同步误差极小的未知参数值,从而在获得待辨识参数的同时实现驱动系统与响应系统的同步。该方法不需要确知驱动系统的参数,不需要驱动系统的所有状态变量,参数收敛速度快。

conjugate gradient method is proposed for parameter identification and chaos synchronization using the drive-response synchronization framework. The scalar drive signal is used to drive a response system with the same structure as that of the drive system and tunable parameters. Chaotic system is extremely sensitive to parameter mismatch, chaotic systems with same structure and different parameters can not synchronize. Therefore, minimizing the synchronization error by adjusting the parameters of response system will eventually lead to synchronization of drive system and response system, at the same time the parameters can be obtained. The conjugate gradient method is adopted to search the real parameters, which make synchronization error minimum, so that the parameters of drive system are identified, and synchronization between drive system and response system occurs. This method is independent on the drive system parameters. Synchronization is accomplished without the need of all state variables of the drive system. The convergence speed of parameters is fast.