# Stability and feasibility of neural network-based controllers via output range analysis

arXiv: https://arxiv.org/abs/2004.00521 · HTML: https://mlsanity.com/paper/2004.00521/

## Key facts

- Cited by 10 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 1 Apr 2020.

## Built on by (most cited first, 10 of 10)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Reliably-stabilizing piecewise-affine neural network controllers](https://mlsanity.com/paper/2111.07183/) (2021)
- [Stability Verification of Neural Network Controllers using Mixed-Integer Programming](https://mlsanity.com/paper/2206.13374/) (2022)
- [Self-Supervised Learning of Iterative Solvers for Constrained Optimization](https://mlsanity.com/paper/2409.08066/) (2024)
- [YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functions](https://mlsanity.com/paper/2505.07054/) (2025)
- [Robust stabilization of polytopic systems via fast and reliable neural network-based approximations](https://mlsanity.com/paper/2204.13209/) (2022)
- [Stochastic Sample Approximations of (Local) Moduli of Continuity](https://mlsanity.com/paper/2509.15368/) (2025)
- [Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorial](https://mlsanity.com/paper/2605.26577/) (2026)
- [Runtime Monitoring and Fault Detection for Neural Network-Controlled Systems](https://mlsanity.com/paper/2403.16132/) (2024)
- [Efficient model predictive control for nonlinear systems modelled by deep neural networks](https://mlsanity.com/paper/2405.10372/) (2024)

## Abstract (arXiv)

Neural networks can be used as approximations of several complex control schemes such as model predictive control. We show in this paper which properties deep neural networks with rectifier linear units as activation functions need to satisfy to guarantee constraint satisfaction and asymptotic stability of the closed-loop system. To do so, we introduce a parametric description of the neural network controller and use a mixed-integer linear programming formulation to perform output range analysis of neural networks. We also propose a novel method to modify a neural network controller such that it performs optimally in the LQR sense in a region surrounding the equilibrium. The proposed method enables the analysis and design of neural network controllers with formal safety guarantees as we illustrate with simulation results.