# Distributionally Robust Lyapunov Function Search Under Uncertainty

arXiv: https://arxiv.org/abs/2212.01554 · HTML: https://mlsanity.com/paper/2212.01554/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2022.

## Built on by (most cited first, 4 of 4)

- [Distributionally Robust Policy and Lyapunov-Certificate Learning](https://mlsanity.com/paper/2404.03017/) (2024)
- [Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions](https://mlsanity.com/paper/2505.10947/) (2025)
- [Trading Devil RL: Backdoor attack via Stock market, Bayesian Optimization and Reinforcement Learning](https://mlsanity.com/paper/2412.17908/) (2024)
- [A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification](https://mlsanity.com/paper/2608.29789/) (2026)

## Abstract (arXiv)

This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints, ensuring that the search for a Lyapunov function remains in the class of SOS polynomial optimization problems. For general systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search. Simulations demonstrate the validity and efficiency of either formulation on non-linear uncertain dynamical systems.