Large gain stability and adaptive expansion estimation in Extremum Seeking

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 ES schemes from their ideal dominant-order average dynamics. The bounds remain valid for possibly large gains. This framework allows us to establish stability and to estimate convergence rates and it opens the way to selecting “optimal” finite gains for ES schemes. Moreover, it constitutes a powerful aid in the design of efficient Perturbation Based ES. We extend this study by providing a simple technique inspired by adaptive control for estimating the cost function derivatives in Numerical Optimization based ES.