In the last decades, many iterative approaches in the field of system identification for control have been proposed. Many successful implementations have been reported, despite the lack of a solid analysis with respect to the convergence and value of these iterations. The aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric H8-norm estimation. The pursued approach involves a novel frequency domain approach that appropriately deals with additive stochastic disturbances and input normalization. The results of the novel convergence analysis are twofold: i) the presence of additive disturbances introduces a bias in the estimation procedure, and ii) the iterative procedure can be interpreted as experiment design for H8-norm estimation, revealing the value of iterations and limits of accuracy in terms of the Fisher information matrix. The results are confirmed by means of a simulation example.
Oomen, T. A. E., Rojas, C. R., Hjalmarsson, H., & Wahlberg, B. (2011). Analyzing Iterations in Identification with application to Nonparametric H-infinity-norm Estimation. In Proceedings of the 18th IFAC World Congress, August 28 - September 2, 2011, Milano, Italy (blz. 9972-9977). Pergamon. https://doi.org/10.3182/20110828-6-IT-1002.02786