Prescribed-Time Newton Extremum Seeking using Delays and Time-Periodic Gains
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| Format: | Preprint |
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2025
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| _version_ | 1866909898835492864 |
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| author | Espitia, Nicolas Poveda, Jorge I. Krstic, Miroslav |
| author_facet | Espitia, Nicolas Poveda, Jorge I. Krstic, Miroslav |
| contents | We study prescribed-time extremum seeking (PT-ES) for scalar maps in the presence of time delays. The PT-ES problem has been studied by Yilmaz and Krstic in 2023 using chirpy probing and time-varying gains that grow unbounded. To alleviate the gain singularity, in this paper we present an alternative approach, employing delays with bounded time-periodic gains, for achieving prescribed-time convergence to the extremum. Our results are not extensions or refinements of earlier works, but a new methodological direction --applicable even when the map has no delay. The main PT-ES algorithm compensates the map's delay and uses perturbation-based and the Newton (rather than gradient) approaches. With the help of averaging theorems in infinite dimension, specifically Retarded Functional Differential Equations (RFDEs), we conduct a prescribed-time convergence analysis on a suitable averaged target ES system, which contains the time-periodic gains of the map and feedback delays. We further extend our method to multivariable static maps and illustrate our results through numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_05464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prescribed-Time Newton Extremum Seeking using Delays and Time-Periodic Gains Espitia, Nicolas Poveda, Jorge I. Krstic, Miroslav Systems and Control Optimization and Control We study prescribed-time extremum seeking (PT-ES) for scalar maps in the presence of time delays. The PT-ES problem has been studied by Yilmaz and Krstic in 2023 using chirpy probing and time-varying gains that grow unbounded. To alleviate the gain singularity, in this paper we present an alternative approach, employing delays with bounded time-periodic gains, for achieving prescribed-time convergence to the extremum. Our results are not extensions or refinements of earlier works, but a new methodological direction --applicable even when the map has no delay. The main PT-ES algorithm compensates the map's delay and uses perturbation-based and the Newton (rather than gradient) approaches. With the help of averaging theorems in infinite dimension, specifically Retarded Functional Differential Equations (RFDEs), we conduct a prescribed-time convergence analysis on a suitable averaged target ES system, which contains the time-periodic gains of the map and feedback delays. We further extend our method to multivariable static maps and illustrate our results through numerical simulations. |
| title | Prescribed-Time Newton Extremum Seeking using Delays and Time-Periodic Gains |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2502.05464 |