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. To design a feedback control system, one has to first develop a model for the relationships among the input variables, potential feedback variables, and the output variables and then select the appropriate variables for feedback control. This is typically done through statistically designed experiments where the input variables are systematically varied, and the experiment is run in an initial, open-loop mode without feedback control. In this paper, we study the optimal design of experiments for modeling such a process. The paper considers a statistical formulation of the problem and studies the structure of optimal designs in the linear case. Locally optimal designs under the D-optimality criteria are studied in detail. A-optimality and Bayesian optimal designs are also discussed. These results are used to characterize the potential loss in efficiency, under various situations, in using the classical optimal designs for this problem.