Title: Constructing Control-Affine Reduced-Order Models Through Autoencoder Learning

Abstract:

This study introduces a novel framework designed for the identification of control-affine reduced-order models (ROMs). Central to this approach is the use of autoencoders (AEs) to map high-dimensional states—and potentially high-dimensional inputs—into lower-dimensional latent representations that are compatible with control-affine state-space dynamics. This transformation is realized through the concurrent training of both the autoencoder and the state-space model. Furthermore, we expand the traditional discrete ROM formulation into a sequence-based architecture. This enhanced model leverages histories of both states and inputs to boost prediction precision without compromising the essential control-affine structure. To demonstrate the utility of our framework, we apply feedback linearization to the resulting models and provide practical guidelines for their efficient implementation. The framework’s efficacy is validated through two numerical case studies, where it is benchmarked against a baseline model that employs an AE to identify a latent space characterized by linear state-space dynamics. The evaluation focuses on two key metrics: the ROM’s prediction accuracy on unseen test data and its capability to effectively steer the system toward a target state or trajectory.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC