  System identification based on Koopman operator theory has grown in
popularity recently. Spectral properties of the Koopman operator of a system
were proven to relate to properties like invariant sets, stability,
periodicity, etc. of the underlying system. Estimation of these spectral
objects has become widely accessible with the numerous algorithms developed in
recent years. We show how one such algorithm -- extended dynamic mode
decomposition -- can be used on data from multiple outputs of a system. These
outputs that are functions of state are called observables in the literature
and could be known outputs like the state itself or unknown outputs like data
from sensors used in systems of biological interest. To this end, we
approximate the desired observables and their iterates in time using minimizers
of regularized least-squares problems which have analytic solutions with
heuristic provisions for expected estimates.
