Extremism Seeking Under Distributed Input Delay

In this paper, we propose an extremum seeking scheme for single-parameter static maps in the presence of distributed input delay. A probing signal is newly developed so that the delayed signal has a conventional form in standard extremum seeking problems. An update law for an estimate of the unknown argument of the extremum is designed based on the idea of the predictor feedback law. We prove the convergence of the estimation error to a neighborhood of the origin by means of the method of averaging. The effectiveness of the proposed scheme is confirmed by a numerical simulation. Copyright (C) 2020 The Authors.