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Learning Control-Affine Reduced-Order Models via Autoencoders

arXiv 2606.05045 ↗First posted 3 Jun 2026math.DS cs.LGcited by 0

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Abstract (arXiv)

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.

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References · 17

  1. 2017GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networkscited by 816
  2. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  3. 2015Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Imagescited by 266
  4. 2017Linearly-Recurrent Autoencoder Networks for Learning Dynamicscited by 142
  5. 2014Dynamic mode decomposition with controlcited by 128
  6. 2023β-Variational autoencoders and transformers for reduced-order modelling of fluid flowscited by 76
  7. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  8. 2021Data-Driven Reduced-Order Modeling of Spatiotemporal Chaos with Neural Ordinary Differential Equationscited by 28
  9. 2022Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constantscited by 24
  10. 2025Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networkscited by 19
  11. 2020Data-Driven Model Predictive Control using Interpolated Koopman Generatorscited by 17
  12. 2014Learning deep dynamical models from image pixelscited by 7
5 more
  1. 2020Non-linear State-space Model Identification from Video Data using Deep Encoderscited by 5
  2. 2025Temporally-Consistent Bilinearly Recurrent Autoencoders for Control Systemscited by 3
  3. 2025Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoderscited by 2
  4. 2022Estimating flow fields with Reduced Order Modelscited by 1
  5. 2024A Feedback Linearized Model Predictive Control Strategy for Input-Constrained Self-Driving Carscited by 1

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