一类三维连续混沌系统的降维反馈同步控制

A High-to Low-Dimension Feedback Synchronization Method for 3-D Continuous Chatio Systems

以线性时变连续系统的稳定性判别方法为依据,针对一类三维连续混沌系统,提出一种降维状态变量反馈同步方法。该方法的基本思想是应用导数不连续的V函数,结合比较原理,把高维时变大系统的稳定性判定,转化为低维定常辅助方程组稳定性判定。其基本步骤主要分为两步:第一步:通过数值仿真来确定状态变量的取值范围;第二步:利用线性化的误差系统来选择状态变量反馈函数和反馈增益,以满足相应Jacob ian矩阵的特征值随时间变化处处具有负实部。并以著名的Lorenz系统为例进行仿真分析,仿真结果表明该方法的有效性。另外,试验结果也表明,同步质量不仅与同步方法有关,也同同步控制函数密切相关。

On the basis of discriminative method of stability＇s in linear time - varying continuous systems, a high - to low - dimension feedback synchronization method is put forward for 3 - D continuous chaotic systems. Main ideal of this method is that a kind of V function whose differential is not continuous is applied, combined the comparable principle, the stability discrimination of high dimensional linear time - varying continuous system can be changed into the stability discrimination of low dimensional linear time - varying continuous system. The method can be divided into two main steps- First, the range of the state variables is determined by the numerical experiments; Secondly, the state variable feedback function and feedback gain can be got by the linear error system which can ensure the eigenvalue of the Jacobian matrix to be always nonpositive with time varying. Experiments for famous Lorenz system demonstrate the effectiveness of this method. Furthermore, experiments can demonstrate that the synchronization quality is not only connected with synchronization method, but also is closely connected with the control function.