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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.00411 |
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| _version_ | 1866929693607854080 |
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| author | Abdallah, Abdallah Ben Dlala, Mohsen |
| author_facet | Abdallah, Abdallah Ben Dlala, Mohsen |
| contents | In this paper, we analyze the output stabilization problem for cascaded nonlinear ODE with $1-d$ heat diffusion equation affected by both in-domain and boundary perturbations. We assume that the only available part of states is the first components of the ODE-subsystem and one boundary of the heat-subsystem. The particularity of this system is two folds i) it contains a nonlinear additive term in the ODE-subsystem, and ii) it is affected by both boundary and in-domain perturbations signals.
For such a system, and unlike the existing works, we succeeded to design an output observer-based feedback that guarantees not only asymptotic stabilization result but also a globally {\it disturbance-to-state stabilization} for our cascaded system. The output feedback is designed using an adequate backstepping transformation recently introduced for coupled ODE-heat equations combined with high-gain observer and high-gain controller. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00411 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Disturbance-to-state stabilization by output feedback of nonlinear ODE cascaded with a reaction-diffusion equation Abdallah, Abdallah Ben Dlala, Mohsen Optimization and Control In this paper, we analyze the output stabilization problem for cascaded nonlinear ODE with $1-d$ heat diffusion equation affected by both in-domain and boundary perturbations. We assume that the only available part of states is the first components of the ODE-subsystem and one boundary of the heat-subsystem. The particularity of this system is two folds i) it contains a nonlinear additive term in the ODE-subsystem, and ii) it is affected by both boundary and in-domain perturbations signals. For such a system, and unlike the existing works, we succeeded to design an output observer-based feedback that guarantees not only asymptotic stabilization result but also a globally {\it disturbance-to-state stabilization} for our cascaded system. The output feedback is designed using an adequate backstepping transformation recently introduced for coupled ODE-heat equations combined with high-gain observer and high-gain controller. |
| title | Disturbance-to-state stabilization by output feedback of nonlinear ODE cascaded with a reaction-diffusion equation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.00411 |