Learning Stabilizing Latent Feedback Controllers via Multi-Step Backward Losses
Abstract
Can learned latent dynamics models support the design of feedback controllers that provably stabilize the original system? For linear time-invariant systems, we show that learning linear autoencoders and latent dynamics with multi-step prediction-reconstruction losses unicodex2014 which we term "backward losses" as they encourage latent trajectories to reconstruct full state trajectories unicodex2014 provably recovers the structure needed for stabilization. Specifically, a sufficiently long reconstruction horizon ensures that a minimum H∞-norm controller designed using the learned latent model stabilizes the original system through output-feedback via the corresponding encoder, provided the latent dimension is large enough to capture all non-stable modes of the underlying system. We also show why both reconstruction and a multi-step horizon are essential: forward prediction losses that require only low prediction error along latent trajectories admit global loss minimizers that discard unstable modes regardless of horizon length, while single-step reconstruction losses can yield latent models whose stabilizing controllers fail to stabilize the original system. Finally, experiments on a non-linear flexible-arm system illustrate the practical implications of our results for learning non-linear autoencoders and latent dynamics.
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BibTeX
@misc{lutkus2026learning,
title = {{Learning Stabilizing Latent Feedback Controllers via Multi-Step Backward Losses}},
author = {Paul Lutkus and Lars Lindemann and Stephen Tu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40931},
eprint = {2610.40931},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40931},
}
RIS
TY - UNPB
TI - Learning Stabilizing Latent Feedback Controllers via Multi-Step Backward Losses
AU - Paul Lutkus
AU - Lars Lindemann
AU - Stephen Tu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40931
UR - https://arxiv.org/abs/2610.40931
AB - Can learned latent dynamics models support the design of feedback controllers that provably stabilize the original system? For linear time-invariant systems, we show that learning linear autoencoders and latent dynamics with multi-step prediction-reconstruction losses unicodex2014 which we term "backward losses" as they encourage latent trajectories to reconstruct full state trajectories unicodex2014 provably recovers the structure needed for stabilization. Specifically, a sufficiently long reconstruction horizon ensures that a minimum H_∞-norm controller designed using the learned latent model stabilizes the original system through output-feedback via the corresponding encoder, provided the latent dimension is large enough to capture all non-stable modes of the underlying system. We also show why both reconstruction and a multi-step horizon are essential: forward prediction losses that require only low prediction error along latent trajectories admit global loss minimizers that discard unstable modes regardless of horizon length, while single-step reconstruction losses can yield latent models whose stabilizing controllers fail to stabilize the original system. Finally, experiments on a non-linear flexible-arm system illustrate the practical implications of our results for learning non-linear autoencoders and latent dynamics.
ER -