aiqbench analysis
This paper gives theoretical grounding for when learned latent dynamics models can safely support feedback control. It shows that multi-step reconstruction losses can recover the structure needed for stabilization in linear systems, while forward-prediction and single-step losses can fail. For ML readers, the useful takeaway is that the training objective, not just model capacity, determines whether a learned model is safe to control with, though the results are proven for linear systems and the nonlinear flexible-arm experiments are only illustrative.
Learning Stabilizing Latent Feedback Controllers via Multi-Step Backward Losses
arXiv:2610.40931v1 Announce Type: cross 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 $\unicode{x2014}$ which we term "backward losses" as they encourage latent trajectories to reconstruct full state trajectories $\unicode{x2014}$ provably recovers the structure needed for stabilization. Specifically, a sufficiently long reconstruction horizon ensures that a minimum ${H}_\infty$-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.
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 $\unicode{x2014}$ which we term "backward losses" as they encourage latent trajectories to reconstruct full state trajectories $\unicode{x2014}$ provably recovers the structure needed for stabilization. Specifically, a sufficiently long reconstruction horizon ensures that a minimum ${H}_\infty$-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.
Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY)
arXiv:2610.40931 [math.OC]
(or arXiv:2610.40931v1 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2610.40931 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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