# Latent Representations for Control Design with Provable Stability and Safety Guarantees

arXiv: https://arxiv.org/abs/2505.23210 · HTML: https://mlsanity.com/paper/2505.23210/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2025.

## Built on by (most cited first, 6 of 6)

- [How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraints](https://mlsanity.com/paper/2511.18606/) (2025)
- [Verification of Unknown Dynamical Systems via Autoencoder Latent Space](https://mlsanity.com/paper/2512.13593/) (2025)
- [Permissive Safety Through Trusted Inference: Verifiable Belief-Space Neural Safety Filters for Assured Interactive Robotics](https://mlsanity.com/paper/2606.02562/) (2026)
- [V-MORALS: Visual Morse Graph-Aided Estimation of Regions of Attraction in a Learned Latent Space](https://mlsanity.com/paper/2602.23524/) (2026)
- [No Free Checker: A Survey of Verifiers for Robot Policies](https://mlsanity.com/paper/2609.09250/) (2026)
- [Latent Safety Filters: When a Lossy Encoder Admits a Transferable Certificate](https://mlsanity.com/paper/2610.04297/) (2026)

## Abstract (arXiv)

We initiate a formal study on the use of low-dimensional latent representations of dynamical systems for verifiable control synthesis. Our main goal is to enable the application of verification techniques -- such as Lyapunov or barrier functions -- that might otherwise be computationally prohibitive when applied directly to the full state representation. Towards this goal, we first provide dynamics-aware approximate conjugacy conditions which formalize the notion of reconstruction error necessary for systems analysis. We then utilize our conjugacy conditions to transfer the stability and invariance guarantees of a latent certificate function (e.g., a Lyapunov or barrier function) for a latent space controller back to the original system. Importantly, our analysis contains several important implications for learning latent spaces and dynamics, by highlighting the necessary geometric properties which need to be preserved by the latent space, in addition to providing concrete loss functions for dynamics reconstruction that are directly related to control design. We conclude by demonstrating the applicability of our theory to two case studies: (1) stabilization of a cartpole system, and (2) collision avoidance for a two vehicle system.