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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.10006 |
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| _version_ | 1866910872786436096 |
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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 |
| id |
arxiv_https___arxiv_org_abs_2503_10006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| 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 |