PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems

TL;DR

This paper presents PINN-Obs, a physics-informed neural network-based observer that adaptively estimates states of nonlinear systems directly from partial, noisy data, with proven convergence and superior performance over traditional methods.

Contribution

The paper introduces a novel adaptive PINN-based observer that integrates system dynamics and sensor data, providing convergence guarantees without requiring explicit system linearization.

Findings

Achieves accurate state estimation in diverse nonlinear systems.

Demonstrates superior robustness and adaptability compared to existing observers.

Provides theoretical convergence guarantees under mild observability conditions.

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.