Non-asymptotic Error Analysis of Subspace Identification for Deterministic Systems
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918128688037888 |
|---|---|
| author | Sun, Shuai |
| author_facet | Sun, Shuai |
| contents | The subspace identification method (SIM) has been extensively employed in the identification of discrete-time multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems. This paper focuses on the analysis of perturbation errors for the system matrices in state-space models and the corresponding system poles, under two unified SIMs, based on a single finite-length input/output sample trajectory. Specifically, we derive non-asymptotic upper bounds on these errors, providing a unified perspective across various SIM variants. Furthermore, we prove that SIMs become ill-conditioned for MIMO systems when the state-to-output dimensionality ratio $n/m$ is large, regardless of system parameters. Finally, numerical experiments are conducted to validate the non-asymptotic results and the ill-conditionedness of SIMs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16761 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-asymptotic Error Analysis of Subspace Identification for Deterministic Systems Sun, Shuai Systems and Control The subspace identification method (SIM) has been extensively employed in the identification of discrete-time multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems. This paper focuses on the analysis of perturbation errors for the system matrices in state-space models and the corresponding system poles, under two unified SIMs, based on a single finite-length input/output sample trajectory. Specifically, we derive non-asymptotic upper bounds on these errors, providing a unified perspective across various SIM variants. Furthermore, we prove that SIMs become ill-conditioned for MIMO systems when the state-to-output dimensionality ratio $n/m$ is large, regardless of system parameters. Finally, numerical experiments are conducted to validate the non-asymptotic results and the ill-conditionedness of SIMs. |
| title | Non-asymptotic Error Analysis of Subspace Identification for Deterministic Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2412.16761 |