# Approximate Robust NMPC using Reinforcement Learning

arXiv: https://arxiv.org/abs/2104.02743 · HTML: https://mlsanity.com/paper/2104.02743/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 6 Apr 2021.

## Builds on (most cited first, 10 of 10)

- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Data-driven Economic NMPC using Reinforcement Learning](https://mlsanity.com/paper/1904.04152/) (2019)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Practical Reinforcement Learning of Stabilizing Economic MPC](https://mlsanity.com/paper/1904.04614/) (2019)
- [Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars](https://mlsanity.com/paper/1711.06586/) (2017)
- [Reinforcement Learning for Mixed-Integer Problems Based on MPC](https://mlsanity.com/paper/2004.01430/) (2020)
- [Reinforcement Learning based on Scenario-tree MPC for ASVs](https://mlsanity.com/paper/2103.11949/) (2021)
- [Reinforcement Learning based on MPC/MHE for Unmodeled and Partially Observable Dynamics](https://mlsanity.com/paper/2103.11871/) (2021)
- [Robust MPC via Min-Max Differential Inequalities](https://mlsanity.com/paper/1611.03924/) (2016)
- [Parallel Explicit Tube Model Predictive Control](https://mlsanity.com/paper/1910.03271/) (2019)

## Built on by (most cited first, 2 of 2)

- [Reinforcement Learning with Model Predictive Control for Highway Ramp Metering](https://mlsanity.com/paper/2311.08820/) (2023)
- [Convergent NMPC-based Reinforcement Learning Using Deep Expected Sarsa and Nonlinear Temporal Difference Learning](https://mlsanity.com/paper/2502.04925/) (2025)

## Abstract (arXiv)

We present a Reinforcement Learning-based Robust Nonlinear Model Predictive Control (RL-RNMPC) framework for controlling nonlinear systems in the presence of disturbances and uncertainties. An approximate Robust Nonlinear Model Predictive Control (RNMPC) of low computational complexity is used in which the state trajectory uncertainty is modelled via ellipsoids. Reinforcement Learning is then used in order to handle the ellipsoidal approximation and improve the closed-loop performance of the scheme by adjusting the MPC parameters generating the ellipsoids. The approach is tested on a simulated Wheeled Mobile Robot (WMR) tracking a desired trajectory while avoiding static obstacles.