Finite Sample Analysis of Open-Loop Subspace Identification Methods

• 成果类型: Article
• 署名作者: He, Jiabao; Ziemann, Ingvar; Rojas, Cristian R.; Qin, S. Joe; Hjalmarsson, Hakan
• 署名单位: Royal Institute of Technology; University of Pennsylvania; Lingnan University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3671690
• 发表日期: 2026
• 关键词: SYSTEM-IDENTIFICATION; asymptotic properties; CONSISTENCY ANALYSIS; algorithms; variance; models

摘要

Subspace identification methods (SIMs) are known for their simple parameterization for MIMO systems and robust numerical properties. However, a comprehensive statistical analysis of SIMs remains an open problem. Following a three-step procedure generally used in SIMs, this work presents a finite sample analysis for open-loop SIMs. In Step 1, we begin with a parsimonious SIM. Leveraging a recent analysis of an individual ARX model, we obtain a union error bound for a Hankel-like matrix constructed from a bank of ARX models. Step 2 involves model reduction via weighted singular value decomposition (SVD), where we use robustness results for SVD to obtain error bounds on extended controllability and observability matrices, respectively. Finally, Step 3 focuses on deriving error bounds for system matrices, where two different realization algorithms, the multivariable output-error state-space type and the CVA type are studied. Our results not only agree with classical asymptotic results, but also show how much data are needed to guarantee a desired error bound with high probability. The proposed method generalizes related finite sample analyses and applies broadly to many variants of SIMs.