Incremental Data Driven Transfer Identification

TL;DR

A geometric method for online transfer identification of a deterministic linear time-invariant system and the effectiveness of the incremental transfer identification paradigm, where identified models with minimal data are used to solve the pole placement problem.

Abstract

We introduce a geometric method for online transfer identification of a deterministic linear time-invariant system. At the beginning of the identification process, we assume access to abundant data from a system that is similar, though not identical, to the true system. In the early stages of data collection from the true system, the dataset generated is still not sufficiently informative to enable precise identification. Consequently, multiple candidate models remain consistent with the observations available at that point. Our method picks, at each instant, the model closest to the similar system that is consistent with the current data. As more data are collected, the proposed model gradually moves away from the initial similar system and eventually converges to the true system when the data set grows to be informative. Numerical examples demonstrate the effectiveness of the incremental transfer identification paradigm, where identified models with minimal data are used to solve the pole placement problem.

Figures (7)

• Figure 1: Illustration of proposed paradigm
• Figure 2: Closest subspace to $U$ containing the vector $a_1$
• Figure 3: Variation of $d(\mathcal{S},\mathcal{H}_i)$ and $d(\mathcal{T}_\Omega,\mathcal{H}_i)$
• Figure 4: Special cases
• Figure 5: Graphical illustration of Example \ref{['eg_scalar1']}