基于高阶累积量的闭环子空间辨识算法研究

为了解决过程噪声和测量噪声为高斯有色噪声且反馈控制器未知情况下的闭环系统辨识问题,给出了基于子空间辨识框架下的闭环辨识算法。算法通过选择适当的辅助变量,构造出噪声过程的高阶累积量,并利用高阶累积量对高斯噪声不敏感的特性来抑制噪声的影响,最后再使用子空间算法辨识系统的状态空间模型。数值仿真表明,对于存在高斯有色噪声的闭环系统,该辨识算法可以得到无偏的系统状态空间模型。

Closed-loop Subspace-based Identification Algorithm Using High Order Cumulants

A closed-loop system identification algorithm was developed in the framework of subspace identification to solve the closed-loop identification problem under colored noises without any knowledge of feedback controller. The key of the developed algorithm was to select a suitable instrumental variable to construct the cross third-order cumulants which were insensitive to any colored Gaussian noises. Then the noise terms can be annihilated and the open-loop state-space models can be recovered by standard subspace identification algorithms. A numerical example demonstrates that constant state-space models are achieved by the proposed algorithm for closed-loop system identification under colored Gaussian-distributed noises.