Combining Exponential and Polynomial Convergence Rates for Accelerated Extremum Seeking: A High-Order Lie Bracket Approach

Victoria Grushkovskaya, Sameh Eisa · 2026 · arXiv

DOI: 10.48550/arXiv.2610.27239 · open-access PDF

Abstract

In this paper, we leverage the recently developed general higher-order Lie bracket approximation theory and framework for control-affine systems to show that we can design extremum seeking (ES) systems that combine flows based on: (i) first-order Lie bracket approximation, which provide an exponential convergence rate for quadratic objective functions and polynomial convergence rate for non-quadratic objective functions; and (ii) higher-order Lie bracket approximation, which provide exponential convergence rate near the minimizer even if the objective function is non-quadratic (i.e., flatter a

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