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

## TL;DR

This paper introduces a sample-based Learning Model Predictive Control approach for uncertain linear systems, enabling safe exploration and performance improvement despite disturbances and constraints.

## Contribution

It extends LMPC to uncertain systems by using noisy data to approximate safe sets and value functions, ensuring safety and robustness.

## Key findings

- Successfully demonstrates safe state space exploration
- Iterative performance improvement under uncertainty
- Robust constraint satisfaction

## Abstract

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.