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arXiv · 2609.06505

Lie bracket approximations of RMSprop for Extremum Seeking Control

Victoria Grushkovskaya·Christian Ebenbauer
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Abstract

This paper presents novel extremum seeking algorithms inspired by RMSProp dynamics and based on Lie bracket approximation techniques. To inherit the behavior of the classical continuous-time RMSProp algorithm, we introduce an extremum seeking scheme that exploits second-order Lie brackets, allowing the excitation of squared gradient terms in the resulting Lie bracket system. Moreover, we propose two modified RMSProp-type algorithms that can be implemented using only first-order Lie bracket approximations, thereby reducing the complexity of the extremum seeking control design. The three resulting extremum seeking algorithms are compared through numerical simulations.

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Victoria Grushkovskaya, Christian Ebenbauer. 2026-09-06. Lie bracket approximations of RMSprop for Extremum Seeking Control. https://arxiv.org/abs/2609.06505

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