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 language | English |
|---|---|
| Pages (from-to) | 4432-4435 |
| Number of pages | 4 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 66 |
| Issue number | 9 |
| DOIs | |
| State | Published - 1 Sep 2021 |
| Externally published | Yes |
Keywords
- Behaviors
- Hankel matrix
- exact system identification
- most powerful unfalsified model (MPUM)
- persistency of excitation
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering