Learning Control-Affine Reduced-Order Models via Autoencoders

2026-06-03

AI Summary

This work addresses the challenge of applying high-dimensional dynamical systems to nonlinear control design by proposing an end-to-end joint training framework that yields low-dimensional, control-affine reduced-order models. The approach employs an autoencoder to map high-dimensional states (and inputs) into a latent space, where a state-space model preserving the control-affine structure is learned. A sequential modeling mechanism is incorporated to integrate historical information, thereby enhancing prediction accuracy. Notably, this method achieves the first joint optimization of an autoencoder with a structurally constrained reduced-order model, enabling advanced control strategies such as feedback linearization. In two numerical case studies, the proposed model significantly outperforms linear dynamic baselines in both predictive accuracy and trajectory tracking performance.

Abstract

We present in this paper a framework for the identification of control-affine reduced-order models (ROMs). The proposed method utilizes autoencoders (AEs) to transform the high-dimensional states, and potentially the high-dimensional inputs, into reduced latent ones suitable for control-affine state-space dynamics. This is achieved by simultaneous training of the AE and the state-space model. In addition, we extend the discrete ROM formulation to a sequence-based model, which processes state and input histories to improve prediction accuracy while preserving the control-affine structure. We motivate our framework by applying feedback linearization to the derived models, and we present guidelines for its efficient use. The proposed framework is assessed on two numerical examples and its performance is compared to a baseline model, where the AE identifies a latent space with linear state-space dynamics. The assessment involves evaluating the prediction accuracy of the ROM on test data and its effectiveness in controlling the system to a desired state or trajectory.

Problem

• control-affine
• reduced-order models
• autoencoders
• high-dimensional systems
• system identification

Innovation

• control-affine
• autoencoder
• reduced-order modeling
• sequence-based modeling
• feedback linearization