Closed-loop Optimal Input Design: the Partial Correlation Approach
Résumé
We consider optimal experiment design for parametric prediction error system identification of linear time-invariant multi-input multi-output systems in closed-loop. The optimization is performed jointly over the controller and the external input. We use a partial correlation approach, i.e. parametrize the set of admissible controller - external input pairs by a finite set of matrix-valued trigonometric moments. Our main contribution is to derive a description of the set of admissible finite-dimensional moment vectors by a linear matrix inequality. Optimal input design problems with constraints and criteria which are linear in these moments can then be cast as semi-definite programs and solved by standard semi-definite programming packages. Our results can be applied to most of the usual model structures, but we assume that the true system is in the model set.