Towards gain tuning for numerical KKL observers

This paper presents a first step towards tuning observers for general nonlinear systems. Relying on recent results around Kazantzis-Kravaris/Luenberger (KKL) observers, we propose an empirical criterion to guide the calibration of the observer, by trading off transient performance and sensitivity to measurement noise. We parametrize the gain matrix and evaluate this criterion over a family of observers for different parameter values. We then use neural networks to learn the mapping between the observer and the nonlinear system, and present a novel method to sample the state-space efficiently for nonlinear regression. We illustrate the merits of this approach in numerical simulations.