# Mapping back and forth between model predictive control and neural networks

arXiv: https://arxiv.org/abs/2404.12030 · HTML: https://mlsanity.com/paper/2404.12030/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 18 Apr 2024.

## Builds on (most cited first, 18 of 18)

- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [Large Scale Model Predictive Control with Neural Networks and Primal Active Sets](https://mlsanity.com/paper/1910.10835/) (2019)
- [Learning Model Predictive Controllers with Real-Time Attention for Real-World Navigation](https://mlsanity.com/paper/2209.10780/) (2022)
- [Near-Optimal Rapid MPC using Neural Networks: A Primal-Dual Policy Learning Framework](https://mlsanity.com/paper/1912.04744/) (2019)
- [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)
- [AReN: Assured ReLU NN Architecture for Model Predictive Control of LTI Systems](https://mlsanity.com/paper/1911.01608/) (2019)
- [Model Predictive Control via On-Policy Imitation Learning](https://mlsanity.com/paper/2210.09206/) (2022)
- [Convex searches for discrete-time Zames-Falb multipliers](https://mlsanity.com/paper/1812.02397/) (2018)
- [Bounding the difference between model predictive control and neural networks](https://mlsanity.com/paper/2204.06486/) (2022)
- [In Proximity of ReLU DNN, PWA Function, and Explicit MPC](https://mlsanity.com/paper/2006.05001/) (2020)
- [Tailored neural networks for learning optimal value functions in MPC](https://mlsanity.com/paper/2112.03975/) (2021)
- [On the Optimal Control of Relaxation Systems](https://mlsanity.com/paper/1909.07219/) (2019)
- [Tailored max-out networks for learning convex PWQ functions](https://mlsanity.com/paper/2206.06826/) (2022)

## Built on by (most cited first, 1 of 1)

- [Convex neural network synthesis for robustness in the 1-norm](https://mlsanity.com/paper/2405.19029/) (2024)

## Abstract (arXiv)

Model predictive control (MPC) for linear systems with quadratic costs and linear constraints is shown to admit an exact representation as an implicit neural network. A method to "unravel" the implicit neural network of MPC into an explicit one is also introduced. As well as building links between model-based and data-driven control, these results emphasize the capability of implicit neural networks for representing solutions of optimisation problems, as such problems are themselves implicitly defined functions.