# Approximate non-linear model predictive control with safety-augmented neural networks

arXiv: https://arxiv.org/abs/2304.09575 · HTML: https://mlsanity.com/paper/2304.09575/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 19 Apr 2023.

## Builds on (most cited first, 19 of 19)

- [A predictive safety filter for learning-based control of constrained nonlinear dynamical systems](https://mlsanity.com/paper/1812.05506/) (2018)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (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)
- [MPC-Net: A First Principles Guided Policy Search](https://mlsanity.com/paper/1909.05197/) (2019)
- [Large Scale Model Predictive Control with Neural Networks and Primal Active Sets](https://mlsanity.com/paper/1910.10835/) (2019)
- [Imitation Learning from MPC for Quadrupedal Multi-Gait Control](https://mlsanity.com/paper/2103.14331/) (2021)
- [Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control](https://mlsanity.com/paper/1912.10360/) (2019)
- [Near-Optimal Rapid MPC using Neural Networks: A Primal-Dual Policy Learning Framework](https://mlsanity.com/paper/1912.04744/) (2019)
- [A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version](https://mlsanity.com/paper/1910.12081/) (2019)
- [Reliably-stabilizing piecewise-affine neural network controllers](https://mlsanity.com/paper/2111.07183/) (2021)
- [Probabilistic performance validation of deep learning-based robust NMPC controllers](https://mlsanity.com/paper/1910.13906/) (2019)
- [Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees](https://mlsanity.com/paper/2004.11184/) (2020)
- [Robust adaptive MPC using control contraction metrics](https://mlsanity.com/paper/2209.11713/) (2022)
- [Safe and Efficient Model Predictive Control Using Neural Networks: An Interior Point Approach](https://mlsanity.com/paper/2203.12196/) (2022)
- [A nonlinear model predictive control framework using reference generic terminal ingredients -- extended version](https://mlsanity.com/paper/1909.12765/) (2019)
- [Learning Stochastic Parametric Differentiable Predictive Control Policies](https://mlsanity.com/paper/2203.01447/) (2022)
- [Approximate Predictive Control Barrier Functions using Neural Networks: A Computationally Cheap and Permissive Safety Filter](https://mlsanity.com/paper/2211.15104/) (2022)
- [Policy Learning for Nonlinear Model Predictive Control with Application to USVs](https://mlsanity.com/paper/2211.10075/) (2022)

## Built on by (most cited first, 9 of 9)

- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Diffusion-Based Approximate MPC: Fast and Consistent Imitation of Multi-Modal Action Distributions](https://mlsanity.com/paper/2504.04603/) (2025)
- [YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functions](https://mlsanity.com/paper/2505.07054/) (2025)
- [Approximate Model Predictive Control for Microgrid Energy Management via Imitation Learning](https://mlsanity.com/paper/2510.20040/) (2025)
- [Certified Speculative Execution for Untrusted AI Agents](https://mlsanity.com/paper/2606.31023/) (2026)
- [Market-Oriented Flow Allocation for Thermal Solar Plants: An Auction-Based Methodology with Artificial Intelligence](https://mlsanity.com/paper/2504.01652/) (2025)
- [Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modeling](https://mlsanity.com/paper/2603.24503/) (2026)
- [All Models are Wrong, Knowing Where is Useful: On Model Uncertainty in Reinforcement Learning](https://mlsanity.com/paper/2606.01363/) (2026)
- [Topological Feasibility Guarantees for Differentiable Predictive Control](https://mlsanity.com/paper/2608.10332/) (2026)

## Abstract (arXiv)

Model predictive control (MPC) achieves stability and constraint satisfaction for general nonlinear systems, but requires computationally expensive online optimization. This paper studies approximations of such MPC controllers via neural networks (NNs) to achieve fast online evaluation. We propose safety augmentation that yields deterministic guarantees for convergence and constraint satisfaction despite approximation inaccuracies. We approximate the entire input sequence of the MPC with NNs, which allows us to verify online if it is a feasible solution to the MPC problem. We replace the NN solution by a safe candidate based on standard MPC techniques whenever it is infeasible or has worse cost. Our method requires a single evaluation of the NN and forward integration of the input sequence online, which is fast to compute on resource-constrained systems. The proposed control framework is illustrated using two numerical non-linear MPC benchmarks of different complexity, demonstrating computational speedups that are orders of magnitude higher than online optimization. In the examples, we achieve deterministic safety through the safety-augmented NNs, where a naive NN implementation fails.