Data driven moment computation, with application to output tracking with external models

This paper addresses the problem of computing the k-moments of a plant from a finite number of measurements of input-output data. The k-moments are (modulo a simple, one-to-one transformation) the values of the transfer matrix and its derivatives computed at specific frequencies, and are instrumental to solve several problems in identification, model reduction, estimation and control. The deterministic setting is considered. At the best of the authors knowledge, in comparison with previously published methods for the same setting, the proposed approach is simpler, is not limited to k-moments with k = 0, and provides exact evaluations of k-moments based only on a finite number of measurements, whereas most competing methods mostly pro- vide estimates that are only asymptotically correct, or require the complete identification of the plant. As a simple application, an output tracking problem is considered, and a solution providing deadbeat convergence is proposed.