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

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.