Uniform quasi-convex optimisation via Extremum Seeking

TL;DR

This paper proves uniformity and stability properties of an extremum seeking scheme, ensuring convergence to the global minimum despite local saddle points, using Fourier series analysis of the average system.

Contribution

It introduces uniformity results for extremum seeking that guarantee semi-global practical stability of the global minimizer.

Findings

Guarantees convergence to the global minimum

Ensures semi-global practical stability

Provides Fourier series-based analysis of the average system

Abstract

The paper deals with a well-known extremum seeking scheme by proving uniformity properties with respect to the amplitudes of the dither signal and of the cost function. Those properties are then used to show that the scheme guarantees the global minimiser to be semi-global practically stable despite the presence of local saddle points. To achieve these results, we analyse the average system associated with the extremum seeking scheme via arguments based on the Fourier series.