On the Optimality and Convergence Properties of the Iterative Learning Model Predictive Controller

TL;DR

This paper analyzes the performance and optimality of Learning Model Predictive Control (LMPC) for linear systems, showing convergence to optimal cost under a verifiable LICQ condition and demonstrating adaptive horizon selection.

Contribution

It introduces a verifiable LICQ condition for LMPC, ensuring performance improvement and convergence, and demonstrates adaptive horizon selection for better control.

Findings

LMPC guarantees asymptotic convergence to optimal cost.

The LICQ condition is easily checkable and applicable to a broad class of systems.

Adaptive horizon selection improves control performance.

Abstract

In this technical note we analyse the performance improvement and optimality properties of the Learning Model Predictive Control (LMPC) strategy for linear deterministic systems. The LMPC framework is a policy iteration scheme where closed-loop trajectories are used to update the control policy for the next execution of the control task. We show that, when a Linear Independence Constraint Qualification (LICQ) condition holds, the LMPC scheme guarantees strict iterative performance improvement and optimality, meaning that the closed-loop cost evaluated over the entire task converges asymptotically to the optimal cost of the infinite-horizon control problem. Compared to previous works this sufficient LICQ condition can be easily checked, it holds for a larger class of systems and it can be used to adaptively select the prediction horizon of the controller, as demonstrated by a numerical example.