Performance Improvement of Extremum Seeking Control using Recursive Least Square Estimation with Forgetting Factor

The main limitation of perturbation based extremum seeking methods is the requirement of a multiple time-scale separation between the system dynamics, the perturbation frequency, and the adaptation rate so as to avoid interactions and possible instabilities. This causes the convergence to be extremely slow. In the present work, we propose a simple modification to the perturbation-based extremum seeking control method that can be used when the system cannot be accurately approximated by a Wiener-Hammerstein model for which convergence rate acceleration schemes are available. The linear filtering used in the perturbation based extremum seeking control for estimating the objective function gradient is replaced by a recursive least square with forgetting factor estimation algorithm. It is shown that this simple modification can accelerate convergence to the optimum by removing one time scale separation.