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

Vikas Kumar Mishra, Ivan Markovsky

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)4432-4435
Number of pages4
JournalIEEE Transactions on Automatic Control
Volume66
Issue number9
DOIs
StatePublished - 1 Sep 2021
Externally publishedYes

Keywords

  • Behaviors
  • exact system identification
  • Hankel matrix
  • most powerful unfalsified model (MPUM)
  • persistency of excitation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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