Learning Control-Affine Reduced-Order Models via Autoencoders
For engineers and researchers working on model reduction for control systems, this work offers a method to learn control-affine ROMs that enable feedback linearization, but it is incremental as it combines existing techniques.
This paper proposes a framework for learning control-affine reduced-order models using autoencoders, achieving improved prediction accuracy and control effectiveness on two numerical examples compared to a baseline with linear latent dynamics.
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.