Learning Causal Estimates of Linear Operators From Noisy Data

• 成果类型: Article
• 署名作者: Cacace, Filippo; Germani, Alfredo
• 署名单位: University Campus Bio-Medico - Rome Italy; University of L'Aquila
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3195151
• 发表日期: 2023
• 页码: 3902-3914
• 关键词: INVERSE PROBLEMS; Machine Learning; sys-tem identification

摘要

This article studies the identification problem of linear systems from a set of noisy input-output trajectories. The problem is formulated and solved as a least-square regularized estimate on a suitable function space of finite-bandwidth operators. This abstract setting is well suited to represent a broad class of finite- and infinite-dimensional linear systems. We determine the value of the regularization parameter as a function of the amount of noise on the learning trajectories and we show how to obtain recursive and causal estimates for the case of linear dynamical systems.