Frequency Selective Weakly-Dual Adaptive Control

Abstract On-line interaction of worst-case identification and control is discussed in this paper on a case study of active noise control. Instead of using some external excitation of the system to improve identification, here the effect of an internal signal on identification is studied. Adaptation of the compensator is performed at a finite set of dominant frequencies of the noise. On-line identification is based on the calculation of polygon bounds of the feasibility sets of complex gains and uncertainties are taken into account. Updating of the compensator is carried out periodically, based on the uncertainty sets of the complex gains. Stability of the combined identification and control scheme is proved. The results presented are in many respect following the literature in the area of frequency selective filtering and adaptation.

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