Asymptotic Variance Expressions for Closed-loop Identification and Their Relevance in Identification for Control

Asymptotic variance expressions are analysed for models that are identified on the basis of closed-loop data. The considered methods comprise the classical ’direct’ and ’indirect’ method, as well as the more recently developed indirect methods, employing coprime factorized models and model parametrizations based on the dual Youla/Kucera parametrization. The variance expressions are compared with the open-loop situation, and evaluated in terms of their relevance for subsequent modelbased control design. Additionally it is specified what is the optimal experimental situation in identification (open-loop or closed-loop), in view of the variance of the resulting model-based controller.