Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks
This is an incremental method for state estimation in control systems, applying PINNs to a known bottleneck in observer design.
The paper tackles the discrete-time nonlinear observer state estimation problem by using Physics-Informed Neural Networks (PINNs) to learn a nonlinear state transformation map within an exact observer linearization framework. The result shows performance assessed via two case studies with analytical comparisons and uncertainty quantification, though no concrete numerical improvements are provided.
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.