Finite dimensional backstepping controller design
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910762765647872 |
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| author | Kalantarov, Varga Özsarı, Türker Yılmaz, Kemal Cem |
| author_facet | Kalantarov, Varga Özsarı, Türker Yılmaz, Kemal Cem |
| contents | We introduce a finite dimensional version of backstepping controller design for stabilizing solutions of PDEs from boundary. Our controller uses only a finite number of Fourier modes of the state of solution, as opposed to the classical backstepping controller which uses all (infinitely many) modes. We apply our method to the reaction-diffusion equation, which serves only as a canonical example but the method is applicable also to other PDEs whose solutions can be decomposed into a slow finite-dimensional part and a fast tail, where the former dominates the evolution in large time. One of the main goals is to estimate the sufficient number of modes needed to stabilize the plant at a prescribed rate. In addition, we find the minimal number of modes that guarantee the stabilization at a certain (unprescribed) decay rate. Theoretical findings are supported with numerical solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02196 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite dimensional backstepping controller design Kalantarov, Varga Özsarı, Türker Yılmaz, Kemal Cem Optimization and Control 35B40, 35K57, 93C20, 93D15, 93D20, 93D23 We introduce a finite dimensional version of backstepping controller design for stabilizing solutions of PDEs from boundary. Our controller uses only a finite number of Fourier modes of the state of solution, as opposed to the classical backstepping controller which uses all (infinitely many) modes. We apply our method to the reaction-diffusion equation, which serves only as a canonical example but the method is applicable also to other PDEs whose solutions can be decomposed into a slow finite-dimensional part and a fast tail, where the former dominates the evolution in large time. One of the main goals is to estimate the sufficient number of modes needed to stabilize the plant at a prescribed rate. In addition, we find the minimal number of modes that guarantee the stabilization at a certain (unprescribed) decay rate. Theoretical findings are supported with numerical solutions. |
| title | Finite dimensional backstepping controller design |
| topic | Optimization and Control 35B40, 35K57, 93C20, 93D15, 93D20, 93D23 |
| url | https://arxiv.org/abs/2309.02196 |