Practical prescribed-time prescribed performance control with asymptotic convergence -- A vanishing sigma-modification approach
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914270474665984 |
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| author | Golestani, Mehdi Song, Yongduan Liu, Weizhen Duan, Guangren Kong, He |
| author_facet | Golestani, Mehdi Song, Yongduan Liu, Weizhen Duan, Guangren Kong, He |
| contents | In this paper, we present a method capable of ensuring practical prescribed-time control with guaranteed performance for a class of nonlinear systems in the presence of time-varying parametric and dynamic uncertainties, and uncertain control coefficients. Our design consists of two key steps. First, we construct a performance-rate function that freezes at and after a user-specified time T, playing a crucial role in achieving desired precision within prescribed time T and dealing with unmodeled dynamics. Next, based on this function and a sigma-modification strategy in which the leakage term starts to vanish at t > T, we develop an adaptive dynamic surface control framework to reduce control complexity, deal with uncertainties, ensure prescribed performance, practical prescribed-time convergence to a specific region, and ultimately achieve asymptotic convergence. The effectiveness of the proposed control method is validated through numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14882 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Practical prescribed-time prescribed performance control with asymptotic convergence -- A vanishing sigma-modification approach Golestani, Mehdi Song, Yongduan Liu, Weizhen Duan, Guangren Kong, He Optimization and Control Systems and Control In this paper, we present a method capable of ensuring practical prescribed-time control with guaranteed performance for a class of nonlinear systems in the presence of time-varying parametric and dynamic uncertainties, and uncertain control coefficients. Our design consists of two key steps. First, we construct a performance-rate function that freezes at and after a user-specified time T, playing a crucial role in achieving desired precision within prescribed time T and dealing with unmodeled dynamics. Next, based on this function and a sigma-modification strategy in which the leakage term starts to vanish at t > T, we develop an adaptive dynamic surface control framework to reduce control complexity, deal with uncertainties, ensure prescribed performance, practical prescribed-time convergence to a specific region, and ultimately achieve asymptotic convergence. The effectiveness of the proposed control method is validated through numerical simulations. |
| title | Practical prescribed-time prescribed performance control with asymptotic convergence -- A vanishing sigma-modification approach |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2601.14882 |