We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a nonlinear state transformation map by solving a system of inhomogeneous functional equations. The performance of the proposed PINN approach is assessed via two illustrative case studies for which the observer linearizing transformation map can be derived analytically. We also perform an uncertainty quantification analysis for the proposed PINN scheme and we compare it with conventional power-series numerical implementations, which rely on the computation of a power series solution.

翻译：我们采用物理信息神经网络（PINNs）求解离散时间非线性观测器的状态估计问题。该方法集成于单步精确观测器线性化框架内，旨在通过求解非齐次泛函方程组来学习非线性状态变换映射。通过两个可解析推导观测器线性化变换映射的案例研究，评估了所提PINN方法的性能。我们进一步对PINN方案进行不确定性量化分析，并与依赖幂级数解计算的经典数值实现方法进行比较。