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arXiv · 2604.03138

Logarithmic Barrier Functions for Practically Safe Extremum Seeking Control

Qixu Wang·Patrick McNamee·Zahra Nili Ahmadabadi
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Abstract

This paper presents a methodology for Practically Safe Extremum Seeking (PSfES), designed to optimize unknown objective functions while strictly enforcing safety constraints via a Logarithmic Barrier Function (LBF). Unlike traditional safety-filtered approaches that may induce chattering, the proposed method augments the cost function with an LBF, creating a repulsive potential that penalizes proximity to the safety boundary. We employ averaging theory to analyze the closed-loop dynamics. A key contribution of this work is the rigorous proof of practical safety for the original system. We establish that the system trajectories remain confined within a safety margin, ensuring forward invariance of the safe set for a sufficiently fast dither signal. Furthermore, our stability analysis shows that the model-free ESC achieves local practical convergence to the modified minimizer strictly within the safe set, through the sequential tuning of small parameters. The theoretical results are validated through numerical simulations.

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Qixu Wang, Patrick McNamee, Zahra Nili Ahmadabadi. 2026-04-03. Logarithmic Barrier Functions for Practically Safe Extremum Seeking Control. https://arxiv.org/abs/2604.03138

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