Extremum seeking based on a Hammerstein-Wiener representation

摘要

This study is concerned with the development of an extremum seeking (ES) strategy based on recursive least square (RLS) for on-line estimation, and a regression model in the form of a Hammerstein-Wiener model. RLS usually provides a faster convergence than the classical bank of filter estimators, and the consideration of process dynamics allows to take account for the phase-shift and attenuation occurring when increasing the frequency of the dither signal. The resulting ES scheme achieves very significant improvement in convergence speed, as illustrated with a numerical example, and a more realistic application to micro-algae cultures in a photo-bioreactor in simulation.