USING OPTIMAL FEEDBACK CONTROL FOR CHAOS TARGETING

Since the conventional open-loop optimal targeting of chaos is very sensitive to noise, a close-loop optimal targeting method is proposed to improve the targeting performance under noise. The present optimal targeting model takes into consideration both precision and speed of the targeting procedure. The parameters, rather than the output, of the targeting controller, are directly optimized to obtain optimal chaos targeting. Analysis regarding the mechanism is given from physics aspect and numerical experiment on the Hénon map is carried out to compare the targeting performance under noise between the close-loop and the open-loop methods.     

特殊矩阵乘积在非线性数值计算中的应用

本文将Hadamard矩阵乘积引入到非线性数值计算,获得了简单的矩阵形式的非线性代数模拟方程,利用Hadamard矩阵乘积和Hadamard矩阵函数的方法,我们能够容易地构造快速收敛的简单迭代法解非线性代数方程组的迭代公式,使该法成为与Newton-Raphson法相比有竞争力的方法,我们也首次定义了一种新的特殊矩阵乘积—SJT矩阵乘积。运用SJT积,我们能够方便高效的计算Newton-Raphson法中Jacobi导数矩阵的精确解,利用Hadamard矩阵乘积的范数性质,我们也导出了非线性计算摄动误差的分析公式,此外,Hadamard积和SJT积能够被用于非线性数值解耦计算,这极大地减少了求解耦合的非线性偏微分方程组的计算工作量和内存需要量。