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

2020/10/28 by Ugo Rosolia, Yingzhao Lian, Rosolia, Ugo +7 · 1 citation
Engineering · Medicine · #Advanced Control Systems Optimization #Cardiovascular Function and Risk Factors #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2010.15153

openalex publication_date 2020/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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