Extremum Seeking with High-Order Lie Bracket Approximations: Achieving Exponential Decay Rate
Optimization and Control
2025-10-28 v3 Dynamical Systems
Abstract
This paper focuses on the further development of the Lie bracket approximation approach for extremum seeking systems. Classical results in this area provide extremum seeking algorithms with exponential convergence rates for quadratic-like cost functions, and polynomial decay rates for cost functions of higher degrees. This paper proposes a novel control design approach that ensures the motion of the extremum seeking system along directions associated with higher-order Lie brackets, thereby ensuring exponential convergence for cost functions that are polynomial-like but with degree greater than two.
Cite
@article{arxiv.2504.01136,
title = {Extremum Seeking with High-Order Lie Bracket Approximations: Achieving Exponential Decay Rate},
author = {Victoria Grushkovskaya and Sameh A. Eisa},
journal= {arXiv preprint arXiv:2504.01136},
year = {2025}
}