# Model-Free Verification for Neural Network Controlled Systems

arXiv: https://arxiv.org/abs/2312.08293 · HTML: https://mlsanity.com/paper/2312.08293/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2023.

## Built on by (most cited first, 2 of 2)

- [Stable and Safe Human-aligned Reinforcement Learning through Neural Ordinary Differential Equations](https://mlsanity.com/paper/2401.13148/) (2024)
- [Robust Verification of Controllers under State Uncertainty via Hamilton-Jacobi Reachability Analysis](https://mlsanity.com/paper/2511.14755/) (2025)

## Abstract (arXiv)

Neural network controllers have shown potential in achieving superior performance in feedback control systems. Although a neural network can be trained efficiently using deep and reinforcement learning methods, providing formal guarantees for the closed-loop properties is challenging. The main difficulty comes from the nonlinear activation functions. One popular method is to use sector bounds on the activation functions resulting in a robust analysis. These methods work well under the assumption that the system dynamics are perfectly known, which is, however, impossible in practice. In this paper, we propose data-driven semi-definite programs to formally verify stability and safety for a neural network controlled linear system with unknown dynamics. The proposed method performs verification directly from end-to-end without identifying the dynamics. Through a numerical example, we validate the efficacy of our method on linear systems with controller trained by imitation learning.