Large Gain Stability of Extremum Seeking and Higher-Order Averaging Theory

TL;DR

This paper develops a framework using averaging theory and contraction analysis to compute explicit bounds on extremum seeking algorithms, enabling stability analysis and optimal gain selection even for large gains.

Contribution

It introduces a novel approach for analyzing extremum seeking stability with large gains, extending beyond small-gain assumptions.

Findings

Explicit bounds on ES deviation from ideal dynamics

Stability and convergence rate estimates for large gains

Guidelines for selecting optimal finite gains

Abstract

Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from its ideal dominant-order average dynamics. The bounds remain valid for possibly large gains. They allow us to establish stability and estimate convergence rates, and they open the way to selecting "optimal" finite gains for the ES scheme.