A non-gradient approach to global extremum seeking: An adaptation of the Shubert algorithm

Abstract

The main purpose of this paper is to adapt the so-called Shubert algorithm for extremum seeking control of general dynamic plants. This algorithm is a good representative of the "sampling optimization methods" that achieve global extremum seeking on compact sets in the presence of local extrema. The algorithm applies to Lipschitz mappings; the model of the system is assumed unknown but the knowledge of its Lipschitz constant is assumed. The controller depends on a design parameter, the "waiting time", and tuning guidelines that relate the design parameter and the region of convergence and accuracy of the algorithm are presented. The analysis shows that semi-global practical convergence (in t..