Optimal algorithms for system identification: a review of recent results

In this paper we present a review of some recent results for identification of linear dynamic systems in the presence of unknown but bounded uncertainty. We make reference to the optimal algorithms theory which provides a general unifying framework to deal with several typical problems of system identification such as model parameter and state estimation, time series prediction and reduced order model estimation. The min-max optimality concepts pertaining to the optimal algorithms theory can be considered as counterparts to those available in classical standard approaches. We review some aspects of the general theory which make it possible to study properties of both classical standard estimators, such as least squares, and optimal error estimators derived in recent work in the field.