# A Neural Network Architecture to Learn Explicit MPC Controllers from Data

arXiv: https://arxiv.org/abs/1911.10789 · HTML: https://mlsanity.com/paper/1911.10789/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2019.

## Built on by (most cited first, 14 of 14)

- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [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)
- [Neural Lyapunov Differentiable Predictive Control](https://mlsanity.com/paper/2205.10728/) (2022)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control](https://mlsanity.com/paper/2306.01914/) (2023)
- [YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functions](https://mlsanity.com/paper/2505.07054/) (2025)
- [Zero-Shot Transferable Solution Method for Parametric Optimal Control Problems](https://mlsanity.com/paper/2509.18404/) (2025)
- [Data-driven Acceleration of MPC with Guarantees](https://mlsanity.com/paper/2511.13588/) (2025)
- [Reinforcement Learning Compensated Model Predictive Control for Off-road Driving on Unknown Deformable Terrain](https://mlsanity.com/paper/2408.09253/) (2024)
- [Data/moment-driven approaches for fast predictive control of collective dynamics](https://mlsanity.com/paper/2402.15611/) (2024)
- [Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control](https://mlsanity.com/paper/2410.00859/) (2024)
- [Neural Networks for on-chip Model Predictive Control: a Method to Build Optimized Training Datasets and its application to Type-1 Diabetes](https://mlsanity.com/paper/2504.11355/) (2025)

## Abstract (arXiv)

We present a methodology to learn explicit Model Predictive Control (eMPC) laws from sample data points with tunable complexity. The learning process is cast in a special Neural Network setting where the coefficients of two linear layers and a parametric quadratic program (pQP) implicit layer are optimized to fit the training data. Thanks to this formulation, powerful tools from the machine learning community can be exploited to speed up the off-line computations through high parallelization. The final controller can be deployed via low-complexity eMPC and the resulting closed-loop system can be certified for stability using existing tools available in the literature. A numerical example on the voltage-current regulation of a multicell DC-DC converter is provided, where the storage and on-line computational demands of the initial controller are drastically reduced with negligible performance impact.