Stochastic parallel model adaptation: theory and applications to active noise canceling, feedforward control, IIR filtering, and identification Academic Article uri icon


  • We consider general stochastic parallel model adaptation problems which consist of an unknown linear time-invariant system and a partially or wholly tunable system connected in parallel, with a common input. The goal of adaptation is to tune the partially tunable system so that its output matches that of the unknown system, despite the presence of any disturbance which is stochastically uncorrelated with the input. Our general formulation of stochastic parallel adaptation schemes allows applications to adaptive feedforward control and adaptive active noise canceling with input contamination, in addition to output error identification and adaptive IIR filtering. We show that in all the applications, the goal of adaptation is met, whenever a matching condition and a positive real condition are satisfied. A special case of our results therefore resolves the long-standing problem of the convergence and the unbiasedness of the output error identification scheme in the presence of colored noise. We also develop a simple general technique for analyzing the strong consistency of parameter estimation with projection. 1992 IEEE

published proceedings

  • IEEE Transactions on Automatic Control

author list (cited authors)

  • Ren, W., & Kumar, P. R.

citation count

  • 17

complete list of authors

  • Ren, W||Kumar, PR

publication date

  • May 1992