A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation
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| Format: | Preprint |
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2025
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| _version_ | 1866918455868915712 |
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| author | Braun, Adam Brivadis, Lucas Auriol, Jean |
| author_facet | Braun, Adam Brivadis, Lucas Auriol, Jean |
| contents | We propose an observer design for a cascaded system composed of an arbitrary nonlinear ordinary differential equation (ODE) with a 1D heat equation. The nonlinear output of the ODE imposes a boundary condition on one side of the heat equation, while the measured output is on the other side. The observer design combines an infinitedimensional Kazantzis-Kravaris/Luenberger (KKL) observer for the ODE with a backstepping observer for the heat equation. This construction is the first extension of the KKL methodology to infinite-dimensional systems. We establish the convergence of the observer under a differential observability condition on the ODE. The effectiveness of the proposed approach is illustrated in numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_04941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation Braun, Adam Brivadis, Lucas Auriol, Jean Optimization and Control We propose an observer design for a cascaded system composed of an arbitrary nonlinear ordinary differential equation (ODE) with a 1D heat equation. The nonlinear output of the ODE imposes a boundary condition on one side of the heat equation, while the measured output is on the other side. The observer design combines an infinitedimensional Kazantzis-Kravaris/Luenberger (KKL) observer for the ODE with a backstepping observer for the heat equation. This construction is the first extension of the KKL methodology to infinite-dimensional systems. We establish the convergence of the observer under a differential observability condition on the ODE. The effectiveness of the proposed approach is illustrated in numerical simulations. |
| title | A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.04941 |