Abstract

Optimal experiment design for system identification was a very active research topic in the 1970’s : the results at that time focused on the minimization of different measures of the parameter covariance matrix. The research on this topic disappeared from the horizon for more than a decade. In the mid eighties new results became available that focused on quality criteria that took account of the objective for which the model was estimated. These results were based on approximate variance formulae for the estimated transfer functions, under the assumption that the model order goes to infinity. Experiment design experienced a sudden revival of activity from around 2003 under a triple influence : the advent of new expressions for the variance of estimated quantities that did not require an assumption of model order going to infinity, the introduction of the concept of « least costly identification design», and the development of new optimal design techniques for identification that convert the optimization problem into semi-definite programs that can be solved using Linear Matrix Inequalities. In this talk we shall first review the development of optimal experiment design. We shall then present new results that allow one to solve 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. Our results are based on the partial positive definite matrix completion theorem.