On-Line Identification via Haar Wavelet Expansions

This paper develops an on-line identification algorithm to estimate system parameters of non-linear continuous time systems. The algorithm, based on Haar wavelet expansions, uses the observed input-output data to estimate unknown system parameters. A recursive formula augmented with indirect matrix-inversion schemes is proposed to substantially reduce computation requisites of an existed offline scheme. By means of the proposed algorithm, the parameter estimates are real-time updated without repeatedly computing matrix inversions. The latter is most timeconsuming in accomplishing every chronological identification operation. The convergences of the off-line and on-line algorithms under noise-free condition are shown. The algorithm is validated through numerical and experimental examples in which the reliability and effectiveness of the proposed approach have been demonstrated. KeywordsOn-line Identification; Haar Wavelet Expansion; Recursive Formula