  This paper traces the strong relations between experimental design and
control, such as the use of optimal inputs to obtain precise parameter
estimation in dynamical systems and the introduction of suitably designed
perturbations in adaptive control. The mathematical background of optimal
experimental design is briefly presented, and the role of experimental design
in the asymptotic properties of estimators is emphasized. Although most of the
paper concerns parametric models, some results are also presented for
statistical learning and prediction with nonparametric models.
