# Neural Networks for Fast Optimisation in Model Predictive Control: A Review

arXiv: https://arxiv.org/abs/2309.02668 · HTML: https://mlsanity.com/paper/2309.02668/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2023.

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

- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retraining](https://mlsanity.com/paper/2404.05835/) (2024)
- [Real-Time Decision-Making for Digital Twin in Additive Manufacturing with Model Predictive Control using Time-Series Deep Neural Networks](https://mlsanity.com/paper/2501.07601/) (2025)
- [Self-Supervised Learning of Iterative Solvers for Constrained Optimization](https://mlsanity.com/paper/2409.08066/) (2024)
- [The Mini Wheelbot: A Testbed for Learning-based Balancing, Flips, and Articulated Driving](https://mlsanity.com/paper/2502.04582/) (2025)
- [Diffusion-Based Approximate MPC: Fast and Consistent Imitation of Multi-Modal Action Distributions](https://mlsanity.com/paper/2504.04603/) (2025)
- [Generative Models From and For Sampling-Based MPC: A Bootstrapped Approach For Adaptive Contact-Rich Manipulation](https://mlsanity.com/paper/2510.14643/) (2025)
- [ReLU Networks for Model Predictive Control: Network Complexity and Performance Guarantees](https://mlsanity.com/paper/2601.16764/) (2026)
- [Behavior Cloning of MPC for 3-DOF Robotic Manipulators](https://mlsanity.com/paper/2606.00383/) (2026)
- [Embedding Linear Equality Constraints in Probabilistic Neural Networks for Dynamic Modelling](https://mlsanity.com/paper/2606.21728/) (2026)

## Abstract (arXiv)

Model Predictive Control (MPC) is an optimal control algorithm with strong stability and robustness guarantees. Despite its popularity in robotics and industrial applications, the main challenge in deploying MPC is its high computation cost, stemming from the need to solve an optimisation problem at each control interval. There are several methods to reduce this cost. This survey focusses on approaches where a neural network is used to approximate an existing controller. Herein, relevant and unique neural approximation methods for linear, nonlinear, and robust MPC are presented and compared. Comparisons are based on the theoretical guarantees that are preserved, the factor by which the original controller is sped up, and the size of problem that a framework is applicable to. Research contributions include: a taxonomy that organises existing knowledge, a summary of literary gaps, discussion on promising research directions, and simple guidelines for choosing an approximation framework. The main conclusions are that (1) new benchmarking tools are needed to help prove the generalisability and scalability of approximation frameworks, (2) future breakthroughs most likely lie in the development of ties between control and learning, and (3) the potential and applicability of recently developed neural architectures and tools remains unexplored in this field.