# Learning for MPC with Stability & Safety Guarantees

arXiv: https://arxiv.org/abs/2012.07369 · HTML: https://mlsanity.com/paper/2012.07369/

## Key facts

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

## Built on by (most cited first, 14 of 14)

- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming](https://mlsanity.com/paper/2406.00592/) (2024)
- [A view on learning robust goal-conditioned value functions: Interplay between RL and MPC](https://mlsanity.com/paper/2502.06996/) (2025)
- [Differentiable Nonlinear Model Predictive Control](https://mlsanity.com/paper/2505.01353/) (2025)
- [Reinforcement Learning with Model Predictive Control for Highway Ramp Metering](https://mlsanity.com/paper/2311.08820/) (2023)
- [Stabilizing reinforcement learning control: A modular framework for optimizing over all stable behavior](https://mlsanity.com/paper/2310.14098/) (2023)
- [Integrating Reinforcement Learning and Model Predictive Control with Applications to Microgrids](https://mlsanity.com/paper/2409.11267/) (2024)
- [Local-Global Learning of Interpretable Control Policies: The Interface between MPC and Reinforcement Learning](https://mlsanity.com/paper/2503.13289/) (2025)
- [GenSafe: A Generalizable Safety Enhancer for Safe Reinforcement Learning Algorithms Based on Reduced Order Markov Decision Process Model](https://mlsanity.com/paper/2406.03912/) (2024)
- [Mission-Aligned Learning-Informed Control of Autonomous Systems: Formulation and Foundations](https://mlsanity.com/paper/2507.04356/) (2025)
- [Model-free Reinforcement Learning for Model-based Control: Towards Safe, Interpretable and Sample-efficient Agents](https://mlsanity.com/paper/2507.13491/) (2025)
- [On Architectures for Combining Reinforcement Learning and Model Predictive Control with Runtime Improvements](https://mlsanity.com/paper/2510.03354/) (2025)
- [Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modeling](https://mlsanity.com/paper/2603.24503/) (2026)
- [A Systematic Review and Taxonomy of Reinforcement Learning-Model Predictive Control Integration for Linear Systems](https://mlsanity.com/paper/2604.21030/) (2026)

## Abstract (arXiv)

The combination of learning methods with Model Predictive Control (MPC) has attracted a significant amount of attention in the recent literature. The hope of this combination is to reduce the reliance of MPC schemes on accurate models, and to tap into the fast developing machine learning and reinforcement learning tools to exploit the growing amount of data available for many systems. In particular, the combination of reinforcement learning and MPC has been proposed as a viable and theoretically justified approach to introduce explainable, safe and stable policies in reinforcement learning. However, a formal theory detailing how the safety and stability of an MPC-based policy can be maintained through the parameter updates delivered by the learning tools is still lacking. This paper addresses this gap. The theory is developed for the generic Robust MPC case, and applied in simulation in the robust tube-based linear MPC case, where the theory is fairly easy to deploy in practice. The paper focuses on Reinforcement Learning as a learning tool, but it applies to any learning method that updates the MPC parameters online.