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Bibliographic Details
Main Authors: Abdelgalil, Mahmoud, Poveda, Jorge I.
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2503.10006
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author Abdelgalil, Mahmoud
Poveda, Jorge I.
author_facet Abdelgalil, Mahmoud
Poveda, Jorge I.
contents We study a novel class of algorithms for solving model-free feedback optimization problems in dynamical systems. The key novelty is the introduction of \emph{persistent resetting learning integrators} (PRLI), which are integrators that are reset at the same frequency at which the plant is dithered using exploratory signals for model-free optimization. It is shown that PRLIs can serve as core mechanisms for real-time gradient estimation in online feedback-optimization tasks where only cost function measurements are available. In particular, unlike existing approaches based on approximation theory, such as averaging or finite-differences, PRLIs can produce global real-time gradient estimates of cost functions, with uniformly bounded perturbations of arbitrarily small magnitude. In this sense, PRLIs function as robust \emph{hybrid} "Oracles" suitable for interconnection with discrete-time optimization algorithms that optimize the performance of continuous-time dynamical plants in closed-loop operation. Compared to existing methods, PRLIs yield \emph{global} stability properties for a broad class of cost functions, surpassing the local or semi-global guarantees offered by traditional approaches based on perturbation and approximation theory. The proposed framework naturally bridges physical systems, modeled as continuous-time plants where continuous exploration is essential, with digital algorithms, represented as discrete-time optimization methods. The main results are illustrated using different numerical examples.
format Preprint
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publishDate 2025
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spellingShingle On Persistently Resetting Learning Integrators: A Framework For Model-Free Feedback Optimization
Abdelgalil, Mahmoud
Poveda, Jorge I.
Optimization and Control
We study a novel class of algorithms for solving model-free feedback optimization problems in dynamical systems. The key novelty is the introduction of \emph{persistent resetting learning integrators} (PRLI), which are integrators that are reset at the same frequency at which the plant is dithered using exploratory signals for model-free optimization. It is shown that PRLIs can serve as core mechanisms for real-time gradient estimation in online feedback-optimization tasks where only cost function measurements are available. In particular, unlike existing approaches based on approximation theory, such as averaging or finite-differences, PRLIs can produce global real-time gradient estimates of cost functions, with uniformly bounded perturbations of arbitrarily small magnitude. In this sense, PRLIs function as robust \emph{hybrid} "Oracles" suitable for interconnection with discrete-time optimization algorithms that optimize the performance of continuous-time dynamical plants in closed-loop operation. Compared to existing methods, PRLIs yield \emph{global} stability properties for a broad class of cost functions, surpassing the local or semi-global guarantees offered by traditional approaches based on perturbation and approximation theory. The proposed framework naturally bridges physical systems, modeled as continuous-time plants where continuous exploration is essential, with digital algorithms, represented as discrete-time optimization methods. The main results are illustrated using different numerical examples.
title On Persistently Resetting Learning Integrators: A Framework For Model-Free Feedback Optimization
topic Optimization and Control
url https://arxiv.org/abs/2503.10006