速度可控的Julia集的同步与参数辨识

摘要

Julia集是分形理论中最重要的分形集之一,有着大量的应用.研究了Julia集的速度可控的同步与参数辨识.基于一阶线性差分方程的稳定性理论,针对响应系统,设计了同步控制器与参数辨识器,并运用极限理论在所设计的同步控制器与参数辨识器上加入了速度控制项,通过调整速度控制项来控制两系统间的同步速度以及驱动系统中所含未知参数的辨识速度.同步控制器控制驱动系统与响应系统达到渐进同步,参数辨识器则控制在驱动系统与响应系统达到渐进同步的过程中辨识出驱动系统中所含的未知参数,从而在驱动系统含有未知参数的情况下,实现两系统间的同步控制.最后,仿真实例表明了方法的有效性和速度可控性.%Julia set is a set of great importance in fractal theory, and has been widely applied. In this paper, speed controllable synchronization and parameter identification of Julia set are researched. Based on the nonlinear feedback controller and the stability theory of first-order linear difference equation, the designs for a generally ap?plicable adaptive synchronization controller and the parameter identifier are obtained. It is proved that the design of the controller for the generalized Julia set achieves the synchronization and unknown parameters of the generalized Julia set can be identified. Meanwhile, the synchronization controller and the parameter identifier are designed with the speed control item which makes the synchronization of drive system and response system and the identification of unknown parameters in the drive system achieve faster. Finally, the simulation examples demonstrate the effective?ness of the methods provided in this paper.