The Set of Linear Time-Invariant Unfalsified Models With Bounded Complexity is Affine

• 成果类型: Article
• 署名作者: Mishra, Vikas Kumar; Markovsky, Ivan
• 署名单位: Vrije Universiteit Brussel
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3046235
• 发表日期: 2021
• 页码: 4432-4435
• 关键词: data models; Complexity theory; time series analysis; Linear systems; Adaptation models; Autonomous systems; kernel; behaviors; exact system identification; Hankel matrix; most powerful unfalsified model (MPUM); persistency of excitation

摘要

We consider exact system identification in the behavioral setting: Given an exact (noise-free) finite time series, find the set of bounded complexity linear time-invariant systems that fit the data exactly. First, we modify the notion of the most powerful unfalsified model for the case of finite data by fixing the number of inputs and minimizing the order. Then, we give necessary and sufficient identifiability conditions, i.e., conditions under which the true data generating system coincides with the most powerful unfalsified model. Finally, we show that the set of bounded complexity exact models is affine: Every exact model is a sum of the most powerful unfalsified model and an autonomous model with bounded complexity.