---
title: "Learning Stabilizing Latent Feedback Controllers via Multi-Step Backward Losses"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2610.40931v1"
permalink: "https://feed.astralor.com/items/itm_6e2a6dd5e4a5b4242ea9828b"
published: "2026-10-29T20:03:49.000Z"
score: 55
channel: "ai"
tags: ["RAG","Learning Stabilizing Latent","Feedback Controllers","Multi-Step Backward Losses","Can","For","Specifically"]
---

# Learning Stabilizing Latent Feedback Controllers via Multi-Step Backward Losses

## 速览

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…

## 关键点

- 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 laten…
- 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 corresp…

## 全文

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.

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