Learning-based model augmentation with LFRs

Artificial neural networks (ANN) have proven to be effective in dealing with the identification nonlinear models for highly complex systems. To still make use of the prior information available from baseline models derived from, e.g., first-principles (FP), methods have been developed that integrate the prior knowledge into the identification algorithm for the ANN in a variety of methods. These methods have shown better estimation speeds and/or accuracy on unseen data. Among these methods are model augmentation structures. A variety of these structures have been considered in literature, there is however no unifying theory to these. In this paper, we propose a flexible linear-fractional-representation (LFR) based model augmentation structure. This model structure is able to represent many common model augmentation structures, thus unifying them under the proposed model structure. Furthermore, we introduce an identification algorithm capable of estimating the proposed model augmentation structure. The performance and generalization capabilities of the identification algorithm and the augmentation structure is demonstrated on a hardening mass-spring-damper simulation example.
Comment: Submitted for CDC 2024