# Learning Model Predictive Control for Iterative Tasks: A Computationally Efficient Approach for Linear System

## TL;DR

This paper introduces an efficient Learning Model Predictive Control method for linear systems that learns from previous iterations to improve performance while reducing computational complexity.

## Contribution

It extends existing LMPC frameworks with a new approach that simplifies computation and guarantees stability using convex safe sets and terminal costs.

## Key findings

- Effective in reducing computational load
- Ensures recursive feasibility and performance improvement
- Validated through simulation results

## Abstract

A Learning Model Predictive Controller (LMPC) for linear system in presented. The proposed controller is an extension of the LMPC [1] and it aims to decrease the computational burden. The control scheme is reference-free and is able to improve its performance by learning from previous iterations. A convex safe set and a terminal cost function are used in order to guarantee recursive feasibility and non-increasing performance at each iteration. The paper presents the control design approach, and shows how to recursively construct the convex terminal set and the terminal cost from state and input trajectories of previous iterations. Simulation results show the effectiveness of the proposed control logic.