# Near-Optimal Rapid MPC using Neural Networks: A Primal-Dual Policy Learning Framework

arXiv: https://arxiv.org/abs/1912.04744 · HTML: https://mlsanity.com/paper/1912.04744/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2019.

## Built on by (most cited first, 16 of 16)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Reliably-stabilizing piecewise-affine neural network controllers](https://mlsanity.com/paper/2111.07183/) (2021)
- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Stability Verification of Neural Network Controllers using Mixed-Integer Programming](https://mlsanity.com/paper/2206.13374/) (2022)
- [Approximate non-linear model predictive control with safety-augmented neural networks](https://mlsanity.com/paper/2304.09575/) (2023)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [Optimality Principles in Spacecraft Neural Guidance and Control](https://mlsanity.com/paper/2305.13078/) (2023)
- [An Improved Data Augmentation Scheme for Model Predictive Control Policy Approximation](https://mlsanity.com/paper/2303.05607/) (2023)
- [EmTract: Extracting Emotions from Social Media](https://mlsanity.com/paper/2112.03868/) (2021)
- [Neural Horizon Model Predictive Control -- Increasing Computational Efficiency with Neural Networks](https://mlsanity.com/paper/2408.09781/) (2024)
- [YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functions](https://mlsanity.com/paper/2505.07054/) (2025)
- [Robust stabilization of polytopic systems via fast and reliable neural network-based approximations](https://mlsanity.com/paper/2204.13209/) (2022)
- [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)
- [Learning Predictive Control with Deep Koopman Operators for Autonomous Vehicle Motion Planning](https://mlsanity.com/paper/2606.08136/) (2026)
- [Towards a Reward-Free Reinforcement Learning Framework for Vehicle Control](https://mlsanity.com/paper/2502.15262/) (2025)

## Abstract (arXiv)

In this paper, we propose a novel framework for approximating the explicit MPC policy for linear parameter-varying systems using supervised learning. Our learning scheme guarantees feasibility and near-optimality of the approximated MPC policy with high probability. Furthermore, in contrast to most existing approaches that only learn the MPC policy, we also learn the "dual policy", which enables us to keep a check on the approximated MPC's optimality online during the control process. If the check deems the control input from the approximated MPC policy safe and near-optimal, then it is applied to the plant, otherwise a backup controller is invoked, thus filtering out (severely) suboptimal control inputs. The backup controller is only invoked with a bounded (low) probability, where the exact probability level can be chosen by the user. Since our framework does not require solving any optimization problem during the control process, it enables the deployment of MPC on resource-constrained systems. Specifically, we illustrate the utility of the proposed framework on a vehicle dynamics control problem. Compared to online optimization methods, we demonstrate a speedup of up to 62x on a desktop computer and 10x on an automotive-grade electronic control unit, while maintaining a high control performance.