Publication [2.2] of Tomás Oliveira e Silva

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Jozsef Bokor, Peter Heuberger, Brett Ninness, Tomás Oliveira e Silva, Paul Van den Hof and Bo Wahlberg, "Modelling and Identification with Orthogonal Basis Functions," Jul. 1999. Workshop notes of a pre-conference tutorial presented at the 14th IFAC World Congress, Beijing, China.


The aim of this workshop is to present a systematic approach to the design and use of flexible orthogonal basis functions in problems of identification and approximation of linear systems, and to show their attractive properties both in theory and in practical (identification) problems.

Decomposing dynamical systems in terms of orthogonal expansions enables the modelling/approximation of the 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. It is shown to have relations with balanced realizations of all-pass (inner) functions. The basis functions are applied in problems of identification, approximation, identification for control (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 = {Bokor, Jozsef} # { and } # {Heuberger, Peter} # { and } #
           {Ninness, Brett} # { and } # {Oliveira e Silva, Tom{\'a}s} #
           { and } # {Van den Hof, Paul} # { and } # {Wahlberg, Bo},
  title = {Modelling and Identification with Orthogonal Basis Functions},
  note = {Workshop notes of a pre-conference tutorial presented at the
         14th~{I}{F}{A}{C} {W}orld {C}ongress, {B}eijing, {C}hina.},
  month = Jul,
  year = {1999}