Data-driven design of embedding observers using automatic differentiation

High gain observers are frequently utilized to estimate the current internal state of nonlinear systems. The approach relies on transforming the system into the observability canonical form and occasionally embedding it into a higher dimensional space. While this can offer advantages in terms of existence conditions and convergence, the computational and implementation tasks are often daunting. In this paper, we address some of these challenges by using neural networks and automatic differentiation to approximate the necessary functions for implementing the observer. This offers a pragmatic approach to bypassing some of the problems associated with embedding observers.