Novel extremum seeking algorithm using Wiener process

We propose a new stochastic continuous time extremum seeking algorithm. The proposed algorithm is simpler to use than conventional stochastic continuous time extremum seeking algorithms. The proposed algorithm uses the Wiener process directly to extract gradients of objective functions. Three schemes, i.e., the simple scheme, the annealing parameter scheme, and the high-pass-filter scheme, are described. We develop a method for estimating the time evolution of the probability density of the solution of the system in the simple scheme. The stability analysis is discussed for the high-pass filter scheme. It is shown that the extreme value of the system is obtained with the proposed system in simulation results.