Stochastic gradient algorithms in active control

This paper deals with some aspects concerning to the practical implementation of the stochastic gradient algorithms in active control. The control system under study is assumed to be a multichannel feedforward system and it is also assumed that there is not feedback signals from the secondary sources measured at the detection sensors. Several iterative algorithms were developed in [1] [2] for a frequency domain model of a multichannel active noise control system. Such iterative algorithms related to the p-norm of the error signal vectors were then applied to control pure tones in time domain [3]. When the disturbance signals can be modelled as stationary stochastic processes, a different framework is needed although there exist some analogies with the frequency domain model. This paper reviews the development and implementation techniques of stochastic gradient algorithms for active control under a general point of view, and then focuses on algorithms called minimax type which were studied in the frequency domain in [1] [2] [3].