Fundamental Limit on SISO System Identification
Fundamental Limit on SISO System Identification
复制标题
SISO 系统识别的基本限制
DOI：
10.1109/cdc51059.2022.9993203
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Yilin Mo
中科院分区：
文献类型：
--
作者：
Jiayun Li;Shuai Sun;Yilin Mo
本文研究了离散时间SISO（SingleInputSingleOutput）系统辨识的基本极限，其中系统的对角标准型由有限个输入输出样本轨迹推导。通过对Cramér-Rao界中Fisher信息矩阵的分析，证明了在系统矩阵的特征值均匀分布的条件下，使用任何无偏估计量的辨识问题的样本复杂度在平均意义下关于系统维数呈超多项式爆炸.此外，我们将我们的结果推广到广泛应用的Ho-Kalman算法，并证明了该算法是病态的高维SISO系统。数值结果进一步验证了本文的结论。
This paper is concerned with the fundamental limit on the identification of discrete-time SISO (Single Input Single Output) system, where the diagonal canonical form of the system is inferred from a finite number of input/output sample trajectories. Through the analysis of the Fisher information matrix used in Cramér-Rao bound, we show that the sample complexity of the identification problem using any unbiased estimator explodes superpolynomially with respect to system dimension in the average sense, assuming that the eigenvalues of the system matrix are uniformly distributed. Furthermore, we extend our result to the widely applied Ho-Kalman algorithm and prove that the algorithm is ill-conditioned for high dimensional SISO systems. Numerical results further demonstrate the conclusion of this paper.