Learning-based augmentation of first-principle models: A linear fractional representation-based approach

Nonlinear system identificationhas proven to be effective in obtaining accurate models from data for complex real-world systems. In particular, recent encoder-based methods with artificial neural network state-space (ANN-SS) models have achieved state-of-the-art performance on various benchmarks, using computationally efficient methods and offering consistent model estimation in the presence of noisy data. However, inclusion of prior knowledge of the system can be further exploited to increase (i) estimation speed, (ii) accuracy, and (iii) interpretability of the resulting models. This paper proposes a model augmentation method that incorporates prior knowledge from first-principles (FP) models in a flexible manner. We introduce a novel linear-fractional-representation (LFR) model structure that allows for the general representation of various augmentation structures including the ones that are commonly used in the literature, and an encoder-based identification algorithm for estimating the proposed structures together with appropriate initialisation methods. The performance and generalisation capabilities of the proposed method are demonstrated on the identification of a hardening mass-spring-damper system in a simulation study and on the data-driven modelling of the dynamics of an F1Tenth electric car using measured data.