High Gain Embedding Observer Design: Combining Differential Geometry and Algebra with Machine Learning

High gain observers are often used for the real-time estimation of the state of nonlinear systems. Several design methods are based on normal forms, which are based on differential geometric considerations. The embedding into a higher dimensional state could be advantageous regarding existence conditions and convergence. However, computation and implementation of such embedding observers is usually significantly more challenging. In this paper, we circumvent some of these problems by employing machine learning. The required functions for the implementation of the observer are approximated by neural networks.