Revisiting Ho-Kalman-Based System Identification: Robustness and Finite-Sample Analysis

• 成果类型: Article
• 署名作者: Oymak, Samet; Ozay, Necmiye
• 署名单位: University of California System; University of California Riverside; University of Michigan System; University of Michigan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3083651
• 发表日期: 2022
• 页码: 1914-1928
• 关键词: Markov processes; Covariance matrices; Complexity theory; trajectory; data models; Task analysis; Robustness; Balanced realization; Markov parameters; Sample Complexity; System identification

摘要

Weconsider the problem of learning a realization for a linear time-invariant (LTI) dynamical system from input/output data. Given a single input/output trajectory, we provide finite time analysis for learning the system's Markov parameters, from which a balanced realization is estimated using the classical Ho-Kalman algorithm. By proving a robustness result for the Ho-Kalman algorithm and combining it with the sample complexity results for Markov parameters, we show how much data are needed to approximate the balanced realization of the system up to a desired accuracy with high probability.