Model adequacy for a precise optimization using extremum seeking control

The perturbation based extremum seeking control is equivalent to fitting a linear model to the data and computing the objective function gradient from this fitted linear model. The present paper asks the question of whether increasing the model complexity e.g., by using a quadratic or a polynomial model of higher order would improve precision. It is shown that when the objective function is available for feedback and provided that the amplitude and the frequency of the excitation signal are sufficiently small, the order of the error made on the optimizing control is independent of the static model order.