# In Proximity of ReLU DNN, PWA Function, and Explicit MPC

arXiv: https://arxiv.org/abs/2006.05001 · HTML: https://mlsanity.com/paper/2006.05001/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

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

- [Mapping back and forth between model predictive control and neural networks](https://mlsanity.com/paper/2404.12030/) (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)

Rectifier (ReLU) deep neural networks (DNN) and their connection with piecewise affine (PWA) functions is analyzed. The paper is an effort to find and study the possibility of representing explicit state feedback policy of model predictive control (MPC) as a ReLU DNN, and vice versa. The complexity and architecture of DNN has been examined through some theorems and discussions. An approximate method has been developed for identification of input-space in ReLU net which results a PWA function over polyhedral regions. Also, inverse multiparametric linear or quadratic programs (mp-LP or mp-QP) has been studied which deals with reconstruction of constraints and cost function given a PWA function.