Rapid stabilization of the heat equation with localized disturbance
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914214178717696 |
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| author | Guzmán, Patricio Parada, Hugo Calle-Cárdenas, Christian |
| author_facet | Guzmán, Patricio Parada, Hugo Calle-Cárdenas, Christian |
| contents | This paper studies the rapid stabilization of a multidimensional heat equation in the presence of an unknown spatially localized disturbance. A novel multivalued feedback control strategy is proposed, which synthesizes the frequency Lyapunov method (introduced by Xiang [41]) with the sign multivalued operator. This methodology connects Lyapunov-based stability analysis with spectral inequalities, while the inclusion of the sign operator ensures robustness against the disturbance. The closed-loop system is governed by a differential inclusion, for which well-posedness is proved via the theory of maximal monotone operators. This approach not only guarantees exponential stabilization but also circumvents the need for explicit disturbance modeling or estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rapid stabilization of the heat equation with localized disturbance Guzmán, Patricio Parada, Hugo Calle-Cárdenas, Christian Systems and Control Analysis of PDEs Optimization and Control This paper studies the rapid stabilization of a multidimensional heat equation in the presence of an unknown spatially localized disturbance. A novel multivalued feedback control strategy is proposed, which synthesizes the frequency Lyapunov method (introduced by Xiang [41]) with the sign multivalued operator. This methodology connects Lyapunov-based stability analysis with spectral inequalities, while the inclusion of the sign operator ensures robustness against the disturbance. The closed-loop system is governed by a differential inclusion, for which well-posedness is proved via the theory of maximal monotone operators. This approach not only guarantees exponential stabilization but also circumvents the need for explicit disturbance modeling or estimation. |
| title | Rapid stabilization of the heat equation with localized disturbance |
| topic | Systems and Control Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2512.19160 |