Convergência não enviesada em controle extremal q-trigonométrico adaptado por q-exponencial

Abstract

Classical extremum seeking (ES) algorithms keep active the permanent search for the presence of a periodic and limited probing signal. However, this structure generates a small periodic bias of the map output to be optimized. In this paper, we propose an algorithm structure perturbed by an adaptive signal with monotonically decreasing amplitude through the Borges q-trigonometry. This structure solves in a simple way the divergences of the increasing adaptation gain of other existing approaches while generating results equivalent to the bias of the signal output without adopting hyperbolic chirps. Furthermore, the proposed methodology has as special cases in the generalized extremum seeking (ESq), classical extremum seeking and unbiased extremum seeking.