基于高增益降维观测器的一类混沌同步

High-gain reduced-order observer-based synchronization for a kind of uncertain chaotic system

针对一类混沌系统,当不满足观测器匹配条件时,讨论了基于观测器的混沌同步及保密通讯问题.通过设计辅助驱动信号,使得观测器匹配条件得以满足.为了处理辅助驱动信号中的未知变量,使用高增益观测器作为近似微分器,不仅给出了辅助驱动信号的估计值,还给出了辅助驱动信号的微分估计值.基于辅助驱动信号的估计值,提出了一种能与非线性项和干扰影响解耦的降维观测器作为响应系统,达到了与驱动系统的同步.在同步的基础上,再基于辅助驱动信号及其微分的估计值,提出了一种保密信息还原的方法.最后,针对Rssler系统进行仿真,仿真结果表明所提出的方法是有效的.

In this paper we consider the issues of chaos synchronization and chaos-based secure communication when the so-called observer matching condition is not satisfied. An auxiliary drive signal vector is introduced such that the observer matching condition is satisfied. High-gain observers are employed to estimate the auxiliary drive signals as well as their derivatives in a finite time by using the drive signals of original system. Then, a kind of reduced-order observer is constructed which can directly eliminate the influence of the non-linear part and the disturbances of the system. Based on the estimates of states as well as the estimates of the auxiliary signals and their derivatives, a kind of message information recovery method is proposed. Finally, the Rrssler chaotic system is used as a simulation example to verify the effectiveness of the proposed method.