Evaluation of the performance of new extremum seeking control algorithm to locate accurately the peaks on multimodal functions

A new Extremum Seeking Control (ESC) scheme is proposed in this paper for multimodal function with two dimension (2D), named as ESC 2D - scheme. This ESC 2D-scheme is a Single Input - Double Outputs (DISO) control system that combine two ESC 1D-schemes of asymptotic perturbed type. Each ESC 1D-scheme has two control loop. The scanning loop generates the signal that sweep the searching space in order to locate the desired peak on the multimodal pattern. The tuning parameter (k
₂
) will define the space of searching. The locating loop generates the gradient signal that will find accurately this peak. The tuning parameter (k
₁
) will define the searching speed under the constraint of stability of the ESC loop. The performance obtained for the ESC 2D scheme proposed is evaluated on multimodal benchmark patterns.