Uncertainty Estimation in Extremum Seeking Control of Unknown Static Maps

Abstract

This letter proposes a design of extremum seeking controllers that guarantees precise convergence of the control system to the unknown optimizer of a measured unknown cost function. The approach introduces an uncertainty estimation technique that provides an estimate of the worst case uncertainty associated with the unknown optimizer. An uncertainty set update algorithm is proposed to reduce the radius of the uncertain set as new data is received. The radius of the uncertainty set is used to reduce the required dither amplitude. The convergence to the unknown optimum and the removal of the dither signal are achieved simultaneously. Asymptotic convergence of the extremum seeking control system to the unknown minimizer is achieved in the absence of measurement noise. A simulation example is provided to demonstrate the effectiveness of the approach.