Continuous-Time Extremum Seeking with Function Measurements Disturbed by Stochastic Noise: A Synchronous Detection Approach

This paper suggests a novel algorithm for extremum seeking based on a stochastic continuous-time optimization approach employing a gradient descent method based on 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 stochastic noise perturbation. The suggested extremum seeking procedure is based on the estimated gradient obtained by the modified stochastic 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 of the suggested extremum seeking algorithm to a zone around the minimizer. To validate the contributions of the paper we present a numerical example.