  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.
