用神经网络自适应学习状态估计增益，提升非线性系统观测精度。
PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems
- 基于物理信息神经网络，直接融合动力学与传感器数据
- 在弱可观测条件下实现状态误差统一最小化
- 适合需要高精度状态估计的控制场景
非线性动态系统的状态估计在控制与工程应用中至关重要，尤其当仅有部分且含噪测量时。本文提出一种新型自适应物理信息神经网络观测器（PINN-Obs），用于非线性系统中的精确状态估计。与传统基于模型的观测器不同，该框架无需显式系统变换或线性化，直接将系统动力学与传感器数据整合进物理信息学习过程。观测器自适应学习最优增益矩阵，确保估计状态收敛至真实状态。严格的理论分析建立了形式化收敛保证，表明在温和可观测条件下，该方法可实现统一误差最小化。通过在多种非线性系统上的大量数值仿真验证了PINN-Obs的有效性，包括异步电机模型、卫星运动系统及经典基准案例。与现有观测器设计的对比实验表明，其在准确性、鲁棒性和适应性方面均表现更优。
原文摘要 · Abstract (English)
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.
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