{"ID":2896511,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.06712","arxiv_id":"2507.06712","title":"PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems","abstract":"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.","short_abstract":"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 nonline...","url_abs":"https://arxiv.org/abs/2507.06712","url_pdf":"https://arxiv.org/pdf/2507.06712v1","authors":"[\"Ayoub Farkane\",\"Mohamed Boutayeb\",\"Mustapha Oudani\",\"Mounir Ghogho\"]","published":"2025-07-09T10:09:45Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.DS\",\"nlin.CD\"]","methods":"[]","has_code":false}