Analyzing iterations in identification with application to nonparametric H∞-norm estimation

  • Authors:

  • Cristian R. Rojas;Tom Oomen;HåKan Hjalmarsson;Bo Wahlberg

  • Affiliations:

  • Automatic Control Lab and ACCESS Linnaeus Center, Electrical Engineering, KTH-Royal Institute of Technology, S-100 44 Stockholm, Sweden;Eindhoven University of Technology, Department of Mechanical Engineering, Control Systems Technology Group, PO Box 513, Building GEM-Z, 5600 MB Eindhoven, The Netherlands;Automatic Control Lab and ACCESS Linnaeus Center, Electrical Engineering, KTH-Royal Institute of Technology, S-100 44 Stockholm, Sweden;Automatic Control Lab and ACCESS Linnaeus Center, Electrical Engineering, KTH-Royal Institute of Technology, S-100 44 Stockholm, Sweden

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2012

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Abstract

Many iterative approaches in the field of system identification for control have been developed. Although successful implementations have been reported, a solid analysis with respect to the convergence of these iterations has not been established. The aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric H"~-norm estimation. The pursued methodology involves a novel frequency domain approach that addresses both additive stochastic disturbances and input normalization. The results of the convergence analysis are twofold: (1) the presence of additive disturbances introduces a bias in the estimation procedure, and (2) the iterative procedure can be interpreted as experiment design for H"~-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.