Safe Adaptive Control of Parabolic PDE-ODE Cascades
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914305629224960 |
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| author | Jiang, Yun Wang, Ji |
| author_facet | Jiang, Yun Wang, Ji |
| contents | In this paper, we propose a safe adaptive boundary control strategy for a class of parabolic partial differential equation-ordinary differential equation (PDE-ODE) cascaded systems with parametric uncertainties in both the PDE and ODE subsystems. The proposed design is built upon an adaptive Control Barrier Function (aCBF) framework that incorporates high-relative-degree CBFs together with a batch least-squares identification (BaLSI)-based adaptive control that guarantees exact parameter identification in finite time. The proposed control law ensures that: (i) if the system output state initially lies within a prescribed safe set, safety is maintained for all time; otherwise, the output is driven back into the safe region within a preassigned finite time; and (ii) convergence to zero of all plant states is achieved. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04656 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Safe Adaptive Control of Parabolic PDE-ODE Cascades Jiang, Yun Wang, Ji Systems and Control In this paper, we propose a safe adaptive boundary control strategy for a class of parabolic partial differential equation-ordinary differential equation (PDE-ODE) cascaded systems with parametric uncertainties in both the PDE and ODE subsystems. The proposed design is built upon an adaptive Control Barrier Function (aCBF) framework that incorporates high-relative-degree CBFs together with a batch least-squares identification (BaLSI)-based adaptive control that guarantees exact parameter identification in finite time. The proposed control law ensures that: (i) if the system output state initially lies within a prescribed safe set, safety is maintained for all time; otherwise, the output is driven back into the safe region within a preassigned finite time; and (ii) convergence to zero of all plant states is achieved. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach. |
| title | Safe Adaptive Control of Parabolic PDE-ODE Cascades |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2602.04656 |