Optimal Experiment Design for Open and Closed-loop System Identification∗

This article reviews the development of experiment design in the field of identification of dynamical systems, from the early work of the seventies on input design for open loop identification to the developments of the last decade that were spurred by the research on identification for control. While the early work focused entirely on criteria based on the asymptotic parameter covariance, the results of the last decade aim at minimizing a wide range of possible criteria, including measures of the estimated transfer function, or of functions of this estimated transfer function. Two important recent developments are the solution of the experiment design problem for closed loop identification, and the formulation and solution of the dual optimal design problem in which the cost of identification is minimized subject to a quality constraint on the estimated model. We shall conclude this survey with new results on the optimal closed loop experiment design problem, where the optimization is performed jointly with respect to the controller and the spectrum of the external excitation.