线性时变系统的状态空间模型递推辨识研究

Recursive identification for state space model of a linear time-varying system

针对线性时变系统中状态空间模型的辨识问题,提出了一种新的模型参数矩阵的递推辨识格式。不同于常用的利用奇异值分解(SVD)或者最小二乘原理计算时变状态空间模型参数的方法,这种新的递推方法基于信号子空间投影原理,通过重新建立输入输出数据之间的关系,构建新的信号子空间矩阵,从而递推得到系统的时变状态空间模型参数。与现有的计算时变状态空间模型的方法相比,这种新的递推方法由于不需要进行SVD的计算,从而大幅的减少了计算时间。特别是当系统的阶次较高时,计算效率优势更为明显。在算例中将这种方法与经典的使用SVD的时变ERA(TV-ERA)方法从辨识结果和计算效率上进行了比较。仿真结果表明这种新的递推算法能有效辨识状态空间方程形式的线性时变系统的模型参数,和TV-ERA方法相比具有更高的计算效率。

A novel recursive identification form for identifying state space model of a linear time-varying system was presented here. Being different from identification methods based on the singular value decomposition（ SVD） and the least square estimation,the proposed recursive method was derived based on the signal subspace projection theory. The time-varying state space model of a system was obtained with the new signal subspace matrix by reconstructing the relation of input and output data. Comparing with the existing identification methods,the computation time of the proposed approach decreased because the recursive method did not require the SVD calculation. Particularly,when the system’s order was high,the advantage of computational efficiency for the recursive method was significant. In numerical simulation examples,the identified results and computational efficiency were compared with those using the classical time-varying eigensystem realization algorithm（ TV-ERA） based on SVD. The simulation results showed that the proposed approach can be applied to identify the state space model of a linear time-varying system and it has a higher computational efficiency than TV-ERA does.