基于多元线性回归的线性系统状态空间辨识算法

A state_space identification algorithm for linear systems based on multivariate linear regression

提出了一种新的多变量线性系统状态空间辨识算法.该算法采用多元线性回归,而不是传统算法中的子空间投影.首先通过多元线性回归获得系统的预估器马尔可夫参数,然后基于一个关键等式获得系统的预估器可观性矩阵与状态序列的乘积矩阵,接着通过奇异值分解得到状态序列,最终再次运用多元线性回归求得系统状态空间模型的各个矩阵.由于本文的算法是预估器式的,因此适用于开环和闭环辨识.基于AIC准则,设计了算法的阶次选择策略,通过仿真例子,验证了该算法的有效性.

This paper gives a novel MIMO statespace identification algorithm for linear systems. Incontrast to traditional algorithms, it is based on multivariate linear regression rather than subspace projection. First, the Markov parameters of the predictor are estimated using multivariate linear regression, then the product of the extended observability matrix and the state sequence is estimated using akey equation, and the state sequence is estimated using singular value decomposition. Finally, the estimates of A, B, C, K matrices are computed again by multivariate regression. Since our algorithm is inpredictor form, it is suitable for both openloop and closedloop cases. The order selection strategies ofthe algorithm are based on the AIC criterion. Numerical experiments show the accuracy of our algorithm.