Behavioral uncertainty quantification for data-driven control

TL;DR

This paper introduces a novel metric for quantifying uncertainty in data-driven control by representing behaviors as subspaces and measuring distances on the Grassmannian, enhancing robustness analysis.

Contribution

It proposes a new finite-time gap metric based on Grassmannian distances for behavioral uncertainty quantification in data-driven control.

Findings

The new metric captures parametric uncertainty in AR models.

Numerical simulations demonstrate improved mode recognition.

The approach offers a robust way to compare behaviors in data-driven control.

Abstract

This paper explores the problem of uncertainty quantification in the behavioral setting for data-driven control. Building on classical ideas from robust control, the problem is regarded as that of selecting a metric which is best suited to a data-based description of uncertainties. Leveraging on Willems' fundamental lemma, restricted behaviors are viewed as subspaces of fixed dimension, which may be represented by data matrices. Consequently, metrics between restricted behaviors are defined as distances between points on the Grassmannian, i.e., the set of all subspaces of equal dimension in a given vector space. A new metric is defined on the set of restricted behaviors as a direct finite-time counterpart of the classical gap metric. The metric is shown to capture parametric uncertainty for the class of autoregressive (AR) models. Numerical simulations illustrate the value of the new metric with a data-driven mode recognition and control case study.