Identifiability in the Behavioral Setting

• 成果类型: Article
• 署名作者: Markovsky, Ivan; Dorfler, Florian
• 署名单位: ICREA; Universitat Politecnica de Catalunya; Centre Internacional de Metodes Numerics en Enginyeria (CIMNE); Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3209954
• 发表日期: 2023
• 页码: 1667-1677
• 关键词: Behavioral sciences; time series analysis; trajectory; kernel; Noise measurement; CONTROLLABILITY; dynamical systems; Behavioral system theory; data-driven representations; most powerful unfalsified model; System identification

摘要

Identifiability, i.e., uniqueness of a solution of the identification problem, is a fundamental issue in system identification and data-driven control. Necessary and sufficient identifiability conditions for deterministic linear time-invariant systems that do not require a priori given input/output partitioning of the variables nor controllability of the true system are derived in the article. The prior knowledge needed for identifiability is the number of inputs, lag, and order of the true system. Our results are based on a modification of the notion of a most powerful unfalsified model for finite data and a novel algorithm for its computation. We provide a generalization of a result that became known as the fundamental lemma and a novel nonparametric data-driven representation of the system behavior based on general data matrix structures. The results assume exact data, however, low-rank approximation allows their application in the case of noisy data. We compare empirically low-rank approximation of the Hankel, Page, and trajectory matrices in the errors-in-variables setting. Although the Page and trajectory matrices are unstructured, the parameter estimates obtained are less accurate than the one obtained from the Hankel matrix.