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.

References in corpus (5)

• Multi-fidelity Bayesian Neural Networks: Algorithms and Applications
• Multi-Objective Loss Balancing for Physics-Informed Deep Learning
• Convergence of Nonlinear Observers on R^n with a Riemannian Metric (Part I)
• Physics-Informed Neural Networks for Time-Domain Simulations: Accuracy, Computational Cost, and Flexibility
• Convergence of Nonlinear Observers on R^n with a Riemannian Metric (Part II)