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

arXiv: https://arxiv.org/abs/2010.15153 · HTML: https://mlsanity.com/paper/2010.15153/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

## Built on by (most cited first, 2 of 2)

- [Deep Neural Koopman Operator-based Economic Model Predictive Control of Shipboard Carbon Capture System](https://mlsanity.com/paper/2504.06818/) (2025)
- [SIT-LMPC: Safe Information-Theoretic Learning Model Predictive Control for Iterative Tasks](https://mlsanity.com/paper/2602.16187/) (2026)

## Abstract (arXiv)

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.