PreprintCC BY 4.0arXiv
Lie bracket approximations of RMSprop for Extremum Seeking Control
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.
Related
- Combining Exponential and Polynomial Convergence Rates for Accelerated Extremum Seeking: A High-Order Lie Bracket Approach
- Extremum Seeking Control: Three Revolutions and the Road Ahead
- Resilient Extremum Seeking Control for Cyber-Physical Systems Under Denial-of-Service Attacks
- Multivariable Extremum Seeking for Locally Lipschitz Objectives
- Distributed Stochastic Extremum Seeking for Optimal Resource Allocation over Networks with Time Delays
BibTeX
@misc{grushkovskaya2026bracket,
title = {{Lie bracket approximations of RMSprop for Extremum Seeking Control}},
author = {Victoria Grushkovskaya and Christian Ebenbauer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06505},
eprint = {2609.06505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06505},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lie bracket approximations of RMSprop for Extremum Seeking Control
AU - Victoria Grushkovskaya
AU - Christian Ebenbauer
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06505
UR - https://arxiv.org/abs/2609.06505
AB - 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.
ER -