Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems

TL;DR

This paper introduces a neural network-based method for designing Luenberger observers for nonlinear systems, enabling more accurate and robust state estimation by approximating complex transformations and their inverses.

Contribution

It proposes a novel supervised physics-informed neural network approach to approximate transformations and their inverses, improving observer design for nonlinear systems.

Findings

Superior generalization compared to existing methods

Robustness to neural network approximation errors

Effective handling of system uncertainties

Abstract

Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output injection. The observer then estimates the system's state in the original coordinates by inverting the transformation map. However, finding a suitable injective transformation whose inverse can be derived remains a primary challenge for general nonlinear systems. We propose a novel approach that uses supervised physics-informed neural networks to approximate both the transformation and its inverse. Our method exhibits superior generalization capabilities to contemporary methods and demonstrates robustness to both neural network's approximation errors and system uncertainties.