# Sample-Based Learning Model Predictive Control for Linear Uncertain Systems

arXiv: https://arxiv.org/abs/1904.06432 · HTML: https://mlsanity.com/paper/1904.06432/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2019.

## Built on by (most cited first, 7 of 7)

- [Lessons from AlphaZero for Optimal, Model Predictive, and Adaptive Control](https://mlsanity.com/paper/2108.10315/) (2021)
- [LS3: Latent Space Safe Sets for Long-Horizon Visuomotor Control of Sparse Reward Iterative Tasks](https://mlsanity.com/paper/2107.04775/) (2021)
- [Safe Model-based Off-policy Reinforcement Learning for Eco-Driving in Connected and Automated Hybrid Electric Vehicles](https://mlsanity.com/paper/2105.11640/) (2021)
- [Adaptive Stochastic Nonlinear Model Predictive Control with Look-ahead Deep Reinforcement Learning for Autonomous Vehicle Motion Control](https://mlsanity.com/paper/2311.04303/) (2023)
- [ZipMPC: Compressed Context-Dependent MPC Cost via Imitation Learning](https://mlsanity.com/paper/2507.13088/) (2025)
- [Safe Deep Model-Based Reinforcement Learning with Lyapunov Functions](https://mlsanity.com/paper/2405.16184/) (2024)
- [SIT-LMPC: Safe Information-Theoretic Learning Model Predictive Control for Iterative Tasks](https://mlsanity.com/paper/2602.16187/) (2026)

## Abstract (arXiv)

We present a sample-based Learning Model Predictive Controller (LMPC) for constrained uncertain linear systems subject to bounded additive disturbances. The proposed controller builds on earlier work on LMPC for deterministic systems. First, we introduce the design of the safe set and value function used to guarantee safety and performance improvement. Afterwards, we show how these quantities can be approximated using noisy historical data. The effectiveness of the proposed approach is demonstrated on a numerical example. We show that the proposed LMPC is able to safely explore the state space and to iteratively improve the worst-case closed-loop performance, while robustly satisfying state and input constraints.