Finite Time Performance Analysis of MIMO Systems Identification

Autor:	Sun, Shuai, Li, Jiayun, Mo, Yilin
Rok vydání:	2023
Předmět:	Electrical Engineering and Systems Science - Systems and Control
Druh dokumentu:	Working Paper
Popis:	This paper is concerned with the finite time identification performance of an n dimensional discrete-time Multiple-Input Multiple-Output (MIMO) Linear Time-Invariant system, with p inputs and m outputs. We prove that the widely-used Ho-Kalman algorithm and Multivariable Output Error State Space (MOESP) algorithm are ill-conditioned for MIMO system when n/m or n/p is large. Moreover, by analyzing the Cramer-Rao bound, we derive a fundamental limit for identifying the real and stable (or marginally stable) poles of MIMO system and prove that the sample complexity for any unbiased pole estimation algorithm to reach a certain level of accuracy explodes superpolynomially with respect to n/(pm). Numerical results are provided to illustrate the ill-conditionedness of Ho-Kalman algorithm and MOESP algorithm as well as the fundamental limit on identification. Comment: 9 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.11790 Zobrazit plný text záznamu View this record from Arxiv