Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2310.11790 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915444950040576 |
|---|---|
| author | Sun, Shuai Li, Jiayun Mo, Yilin |
| author_facet | Sun, Shuai Li, Jiayun Mo, Yilin |
| contents | This paper is concerned with the finite sample 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 systems 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11790 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite Sample Performance Analysis of MIMO Systems Identification Sun, Shuai Li, Jiayun Mo, Yilin Systems and Control This paper is concerned with the finite sample 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 systems 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. |
| title | Finite Sample Performance Analysis of MIMO Systems Identification |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2310.11790 |