# Large Scale Model Predictive Control with Neural Networks and Primal Active Sets

arXiv: https://arxiv.org/abs/1910.10835 · HTML: https://mlsanity.com/paper/1910.10835/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2019.

## Built on by (most cited first, 29 of 29)

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- [Amortized Global Search for Efficient Preliminary Trajectory Design with Deep Generative Models](https://mlsanity.com/paper/2308.03960/) (2023)
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- [Approximate non-linear model predictive control with safety-augmented neural networks](https://mlsanity.com/paper/2304.09575/) (2023)
- [Neural Lyapunov Differentiable Predictive Control](https://mlsanity.com/paper/2205.10728/) (2022)
- [Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retraining](https://mlsanity.com/paper/2404.05835/) (2024)
- [Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming](https://mlsanity.com/paper/2406.00592/) (2024)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [AC4MPC: Actor-Critic Reinforcement Learning for Nonlinear Model Predictive Control](https://mlsanity.com/paper/2406.03995/) (2024)
- [Diffusion Policies for Generative Modeling of Spacecraft Trajectories](https://mlsanity.com/paper/2501.00915/) (2025)
- [Self-Supervised Learning of Iterative Solvers for Constrained Optimization](https://mlsanity.com/paper/2409.08066/) (2024)
- [Learning Multiple Initial Solutions to Optimization Problems](https://mlsanity.com/paper/2411.02158/) (2024)
- [Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding](https://mlsanity.com/paper/2512.01565/) (2025)
- [An Improved Data Augmentation Scheme for Model Predictive Control Policy Approximation](https://mlsanity.com/paper/2303.05607/) (2023)
- [Warm-starting active-set solvers using graph neural networks](https://mlsanity.com/paper/2511.13174/) (2025)
- [On Building Myopic MPC Policies using Supervised Learning](https://mlsanity.com/paper/2401.12546/) (2024)
- [Mapping back and forth between model predictive control and neural networks](https://mlsanity.com/paper/2404.12030/) (2024)
- [GLENS: Global Search via Learning from Solver Iterates with Diffusion Models](https://mlsanity.com/paper/2606.00366/) (2026)
- [CIKAN: Constraint Informed Kolmogorov-Arnold Networks for Autonomous Spacecraft Rendezvous using Time Shift Governor](https://mlsanity.com/paper/2412.03710/) (2024)
- [Learning Robust Satellite Attitude Dynamics with Physics-Informed Normalising Flow](https://mlsanity.com/paper/2508.07841/) (2025)
- [ReLU Networks for Model Predictive Control: Network Complexity and Performance Guarantees](https://mlsanity.com/paper/2601.16764/) (2026)
- [Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modeling](https://mlsanity.com/paper/2603.24503/) (2026)
- [LAtent Phase Inference from Short time sequences using SHallow REcurrent Decoders (LAPIS-SHRED)](https://mlsanity.com/paper/2604.01216/) (2026)
- [Amortising Trajectory Optimisation for Residual MPC via Implicit Contact Differentiation](https://mlsanity.com/paper/2607.24959/) (2026)
- [RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environments](https://mlsanity.com/paper/2609.39854/) (2026)
- [Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering](https://mlsanity.com/paper/2610.02014/) (2026)

## Abstract (arXiv)

This work presents an explicit-implicit procedure to compute a model predictive control (MPC) law with guarantees on recursive feasibility and asymptotic stability. The approach combines an offline-trained fully-connected neural network with an online primal active set solver. The neural network provides a control input initialization while the primal active set method ensures recursive feasibility and asymptotic stability. The neural network is trained with a primal-dual loss function, aiming to generate control sequences that are primal feasible and meet a desired level of suboptimality. Since the neural network alone does not guarantee constraint satisfaction, its output is used to warm start the primal active set method online. We demonstrate that this approach scales to large problems with thousands of optimization variables, which are challenging for current approaches. Our method achieves a 2x reduction in online inference time compared to the best method in a benchmark suite of different solver and initialization strategies.