Valery Morgenthaler | Searcharxiv

arXiv2023

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.

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arXiv2023

Recognition Models to Learn Dynamics from Partial Observations with Neural ODEs

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary differential equations can be written as a flexible framework for system identification and can incorporate a broad spectrum of physical insight, giving physical interpretability to the resulting latent space. In the case of partial observations, however, the data points cannot directly be mapped to the latent state of the ODE. Hence, we propose to design recognition models, in particular inspired by nonlinear observer theory, to link the partial observations to the latent state. We demonstrate the performance of the proposed approach on numerical simulations and on an experimental dataset from a robotic exoskeleton.

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