Publication [6.16] of Tomás Oliveira e Silva

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Paul Van den Hof, Bo Wahlberg, Peter Heuberger, Brett Ninness, Jozsef Bokor and Tomás Oliveira e Silva, "Modelling and Identification with Rational Orthogonal Basis Functions," System Identification (SYSID 2000), vol. 2, pp. 445-456, 2000.


Decomposing dynamical systems in terms of orthogonal expansions enables the modelling/approximation of a system with a finite length expansion. By flexibly tuning the basis functions to underlying system characteristics, the rate of convergence of these expansions can be drastically increased, leading to highly accurate models (small bias) being represented by few parameters (small variance). Additionally algorithmic and numerical aspects are favourable.

A recently developed general theory for basis construction will be presented, that is a generalization of the classical Laguerre theory. The basis functions are applied in problems of identification, approximation, realization, uncertainty modelling, and adaptive filtering, particularly exploiting the property that basis function models are linearly parametrized. Besides powerful algorithms, they also provide useful analysis tools for understanding the underlying identification/approximation algorithms.

BibTeX entry

  author = {Van den Hof, Paul} # { and } # {Wahlberg, Bo} # { and } #
           {Heuberger, Peter} # { and } # {Ninness, Brett} # { and } # {Bokor,
           Jozsef} # { and } # {Oliveira e Silva, Tom{\'a}s},
  title = {Modelling and Identification with Rational Orthogonal Basis
  booktitle = {System Identification (SYSID 2000)},
  year = {2000},
  editor = {Smith, Roy},
  volume = {2},
  pages = {445--456},
  publisher = {Pergamon}