Numerical design of Luenberger observers for nonlinear systems

In this paper, we propose a method to numerically design observers for nonlinear systems. The method relies on the theory of nonlinear Luenberger observers, which consist in mapping the nonlinear dynamics to a linear system, for which observer design is easy. Relying on results guaranteeing the existence of such mappings, we propose to approximate them by performing nonlinear regression on data simply generated by solving the system and observer dynamics. We detail different approaches for autonomous and excited systems and the choices made for data generation, pre-processing, and regression.