Latent Representations for Control Design with Provable Stability and Safety Guarantees

2025/05/29 by Paul Lutkus, Kaiyuan Wang, Lutkus, Paul +5 · 2 citations
Computer Science · Physics and Astronomy · #Adversarial Robustness in Machine Learning #FOS: Electrical engineering #FOS: Mathematics #Formal Methods in Verification #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2505.23210

openalex publication_date 2025/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions
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• Representation Learning: A Review and New Perspectives

Cited by

• Verification of Unknown Dynamical Systems via Autoencoder Latent Space
• How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraints

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