Design of neural high-gain observers for autonomous nonlinear systems using universal differential equations

The main goal of this paper is to introduce universal high-gain observers for nonlinear autonomous systems in observability canonical form. After a brief review of observability concepts for nonlinear autonomous systems and of results taken from the literature about universal differential equations, a universal high-gain observer for autonomous nonlinear systems is proposed. Its design is carried out by using universal differential equations both to estimate the dynamics in observability canonical form of the plant and to design the (time-varying) gain of the observer. Different training methods are proposed to efficiently tune the universal differential equations involved in the design. The practical effectiveness of this observer is demonstrated through several numerical examples.