Gradient-based stochastic extremum seeking for static maps with delays

This paper presents a Gradient-based stochastic extremum seeking method for unknown mappings with known time delays. We design a new predictor for feedback delay compensation. It also has local exponential stability when it converges to an unknown extremum. The stability analysis is camed out by inversion transformation and infinite dimension averaging method, and the infinite dimension state caused by time delay is obtained. In addition, the simulation results show the effectiveness of the proposed scheme.