Extremum Seeking using Synchronous Detection Method with Time-Varying Parameters

The authors suggest an algorithm for extremum seeking based on a random process optimization approach employing a gradient descent method with the synchronous detection technique. The problem consists on finding the minimum of a strongly convex function which is unknown but may be measured in any testing point subject to a noise perturbation. The suggested extremum seeking procedure is based on the estimated gradient obtained by the modified version of the Synchronous Detection Method. We have added a first order low-pass filter to the gradient estimator to attenuate the noise in the estimations. We prove the mean-squared convergence in probability of the suggested algorithm. To validate the contributions of the paper we present a numerical example.