Input-to-State Stabilization of 1-D Parabolic PDEs under Output Feedback Control
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913393425776640 |
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| author | Bi, Yongchun Zheng, Jun Zhu, Guchuan |
| author_facet | Bi, Yongchun Zheng, Jun Zhu, Guchuan |
| contents | This paper addresses the problem of input-to-state stabilization for a class of parabolic equations with time-varying coefficients, as well as Dirichlet and Robin boundary disturbances. By using time-invariant kernel functions, which can reduce the complexity in control design and implementation, an observer-based output feedback controller is designed via backstepping. By using the generalized Lyapunov method, which can be used to handle Dirichlet boundary terms, the input-to-state stability of the closed-loop system under output feedback control, as well as the state estimation error system, is established in the spatial $L^\infty$-norm. Numerical simulations are conducted to confirm the theoretical results and to illustrate the effectiveness of the proposed control scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Input-to-State Stabilization of 1-D Parabolic PDEs under Output Feedback Control Bi, Yongchun Zheng, Jun Zhu, Guchuan Optimization and Control Analysis of PDEs This paper addresses the problem of input-to-state stabilization for a class of parabolic equations with time-varying coefficients, as well as Dirichlet and Robin boundary disturbances. By using time-invariant kernel functions, which can reduce the complexity in control design and implementation, an observer-based output feedback controller is designed via backstepping. By using the generalized Lyapunov method, which can be used to handle Dirichlet boundary terms, the input-to-state stability of the closed-loop system under output feedback control, as well as the state estimation error system, is established in the spatial $L^\infty$-norm. Numerical simulations are conducted to confirm the theoretical results and to illustrate the effectiveness of the proposed control scheme. |
| title | Input-to-State Stabilization of 1-D Parabolic PDEs under Output Feedback Control |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2406.11264 |