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

被引：6

作者：

Mishra, Vikas Kumar ^{[1
]}

Markovsky, Ivan ^{[1
]}

机构：

[1] Vrije Univ Brussel, Dept ELEC, B-1050 Brussels, Belgium

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2021年 / 66卷 / 09期

基金：

欧洲研究理事会;

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; BEHAVIORAL-APPROACH; SYSTEM;

D O I：

10.1109/TAC.2020.3046235

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

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.

引用

页码：4432 / 4435

页数：4

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