Convex relaxation of sequential optimal input design for a class of structured large-scale systems: process gain estimation

This paper considers optimal input design for a class of structured large-scale systems in which the input-output directionality is independent of frequency. For maximizing the information contained in experimental data collected from applying inputs to the process, manipulated variables are computed from solving constrained optimizations for which the payoff function is related to the covariance of estimation or a user-specified quality measure of estimation and the constraints correspond to requirements for operational safety and actuator limitations. The methods are applied to process gain estimation for a simulated blown film process to illustrate the input design procedure and compare the results for two different types of constraint sets. In addition, closed-form solutions are computed for the optimal input design associated with signal-to-noise ratio, D-optimality, and A-optimality measures in the presence of an input sum-of-squares constraint. A new measure for sensitivity of optimality criteria to the change in input direction is introduced and computed for the three aforementioned optimality criteria.