  In this paper, the classical algebraic regulator problem is studied in a
data-driven context. The endosystem is assumed to be an unknown system that is
interconnected to a known exosystem that generates disturbances and reference
signals. The problem is to design a regulator so that the output of the
(unknown) endosystem tracks the reference signal, regardless of its initial
state and the incoming disturbances. In order to do this, we assume that we
have a set of input-state data on a finite time-interval. We introduce the
notion of data informativity for regulator design, and establish necessary and
sufficient conditions for a given set of data to be informative. Also, formulas
for suitable regulators are given in terms of the data. Our results are
illustrated by means of two extended examples.
