结构未知系统降维辨识方法——变量消去算法

A reduced-dimension identification algorithm for systems with unknown structures:Variable elimination algorithm

针对结构未知的系统提出一种新的降维辨识方法.借助核函数方法,利用一个高维Volterra模型逼近未知系统.由于Volterra模型未知参数维数较高,为避免高阶矩阵求逆和求特征值,提出变量消去算法,将高维系统的辨识问题转化为两个低维系统辨识问题.通过理论证明采用降维算法后降维系统信息矩阵条件数变小,参数收敛速度得到提高.进一步引入Aitken加速方法提高算法收敛速度,增强算法对步长的鲁棒特性.最后通过仿真例子验证所提出方法的有效性.

This study proposes a reduced-dimension identification algorithm for systems with unknown structures.By using the kernel method,the unknown structure systems are approximated by a Volterra model with a high-dimension.To avoid high-order matrix inverse and eigenvalue calculations,a variable elimination algorithm is developed,which decomposes the high-dimension model into two sub-models.The theoretical analysis shows that the variable elimination algorithm has a faster convergence rate than that of the traditional gradient descent algorithm.In addition,an Aitken method is introduced to increase the convergence rates and to make the algorithm be robust to the step-size.The simulation results verify the effectiveness of the algorithm.