PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918178054995968 |
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| author | Farkane, Ayoub Boutayeb, Mohamed Oudani, Mustapha Ghogho, Mounir |
| author_facet | Farkane, Ayoub Boutayeb, Mohamed Oudani, Mustapha Ghogho, Mounir |
| contents | State estimation for nonlinear dynamical systems is a critical challenge in control and engineering applications, particularly when only partial and noisy measurements are available. This paper introduces a novel Adaptive Physics-Informed Neural Network-based Observer (PINN-Obs) for accurate state estimation in nonlinear systems. Unlike traditional model-based observers, which require explicit system transformations or linearization, the proposed framework directly integrates system dynamics and sensor data into a physics-informed learning process. The observer adaptively learns an optimal gain matrix, ensuring convergence of the estimated states to the true system states. A rigorous theoretical analysis establishes formal convergence guarantees, demonstrating that the proposed approach achieves uniform error minimization under mild observability conditions. The effectiveness of PINN-Obs is validated through extensive numerical simulations on diverse nonlinear systems, including an induction motor model, a satellite motion system, and benchmark academic examples. Comparative experimental studies against existing observer designs highlight its superior accuracy, robustness, and adaptability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06712 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems Farkane, Ayoub Boutayeb, Mohamed Oudani, Mustapha Ghogho, Mounir Machine Learning Dynamical Systems Chaotic Dynamics State estimation for nonlinear dynamical systems is a critical challenge in control and engineering applications, particularly when only partial and noisy measurements are available. This paper introduces a novel Adaptive Physics-Informed Neural Network-based Observer (PINN-Obs) for accurate state estimation in nonlinear systems. Unlike traditional model-based observers, which require explicit system transformations or linearization, the proposed framework directly integrates system dynamics and sensor data into a physics-informed learning process. The observer adaptively learns an optimal gain matrix, ensuring convergence of the estimated states to the true system states. A rigorous theoretical analysis establishes formal convergence guarantees, demonstrating that the proposed approach achieves uniform error minimization under mild observability conditions. The effectiveness of PINN-Obs is validated through extensive numerical simulations on diverse nonlinear systems, including an induction motor model, a satellite motion system, and benchmark academic examples. Comparative experimental studies against existing observer designs highlight its superior accuracy, robustness, and adaptability. |
| title | PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems |
| topic | Machine Learning Dynamical Systems Chaotic Dynamics |
| url | https://arxiv.org/abs/2507.06712 |