Wavelet amendment of polynomial models in hammerstein systems identification

Przemysław Śliwiński, Jerzy Rozenblit, Michael W. Marcellin, Ryszard Klempous

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


A new wavelet algorithm for on-line improvement of an existing polynomial model of nonlinearity in a Hammerstein system is proposed and its properties are examined. The algorithm employs wavelet bases on interval. Convergence of the resulting assembly, comprising the parametric polynomial model and a nonparametric wavelet add-on, to the system nonlinearity is shown. Rates of convergence for uniformly smooth and piecewise smooth nonlinearities with discontinuities are both established.

Original languageEnglish (US)
Pages (from-to)820-825
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number4
StatePublished - 2009


  • Hammerstein system
  • Nonlinear system identification
  • Order statistics
  • Polynomial models
  • Semiparametric approach
  • Wavelet bypass
  • Wavelet regression estimate

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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