Fixed-Time Gradient-Based Extremum Seeking
Jorge I. Poveda, Miroslav Krstić
Abstract
In this paper, we present the first averaging-based extremum seeking controller able to achieve semi-global practical fixed-time asymptotic stability in static maps, where by fixed-time asymptotic stability we mean convergence via a KL bound that has a finite-time convergence property with a uniformly bounded settling time. In general, this property cannot be achieved by standard smooth extremum seeking algorithms having a Lipschitz continuous average system. The extremum seeking dynamics are based on an underlying average system that is a perturbed version of a continuous gradient flow with prescribed finite-time convergence properties, recently studied in the literature. In order to study the stability properties of the ES dynamics, we make use of averaging tools for nonsmooth dynamical systems, which allow us to link the KL bound of the average system with the KL bound that characterizes the convergence properties of the ES dynamics. Numerical simulations illustrate our results.