Robust Learning Model Predictive Control for Linear Systems Performing Iterative Tasks

TL;DR

This paper introduces a robust Learning Model Predictive Control approach for linear systems with uncertainties, utilizing historical data to iteratively improve control policies while ensuring safety, stability, and performance bounds.

Contribution

It presents a novel iterative LMPC design that leverages data to enlarge control domains and guarantees robustness and stability for uncertain linear systems.

Findings

Enlarges control domain iteratively using historical data.

Guarantees recursive constraint satisfaction and stability.

Demonstrates effectiveness on a linear system with disturbances.

Abstract

A robust Learning Model Predictive Controller (LMPC) for uncertain systems performing iterative tasks is presented. At each iteration of the control task the closed-loop state, input and cost are stored and used in the controller design. This paper first illustrates how to construct robust invariant sets and safe control policies exploiting historical data. Then, we propose an iterative LMPC design procedure, where data generated by a robust controller at iteration $j$ are used to design a robust LMPC at the next $j+1$ iteration. We show that this procedure allows us to iteratively enlarge the domain of the control policy and it guarantees recursive constraints satisfaction, input to state stability and performance bounds for the certainty equivalent closed-loop system. The use of an adaptive prediction horizon is the key element of the proposed design. The effectiveness of the proposed control scheme is illustrated on a linear system subject to bounded additive disturbance.