Optimal Design of Experiments for Modeling Processes with Feedback Control Variables

Feedback control schemes have been widely used in many engineering applications for a long time. Despite this, there has been very little work done on eecient design of experiments for modeling feedback control processes in order to select the appropriate feedback variables. This paper considers a general statistical formulation of this problem and studies the properties of optimal designs in the rst-order case. Locally optimal designs under A? and D?optimality criteria as well as Bayesian optimal designs are developed. These results are used to characterize the properties of these designs and to contrast them with traditional optimal designs without feedback variables. In particular, the relative eeciency of the traditional designs is studied for various situations of practical interest.