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

Rosolia, Ugo and Lian, Yingzhao and Maddalena, Emilio T. and Ferrari-Trecate, Giancarlo and Jones, Colin N. (2020) On the Optimality and Convergence Properties of the Iterative Learning Model Predictive Controller. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210716-225824511

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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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2010.15153arXivDiscussion Paper
ORCID:
AuthorORCID
Rosolia, Ugo0000-0002-1682-0551
Alternate Title:On the Optimality and Convergence Properties of the Learning Model Predictive Controller
Additional Information:This work has received support from the Swiss National Science Foundation under the RISK project (Risk Aware Data-Driven Demand Response), grant number 200021 175627.
Funders:
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)200021_175627
Record Number:CaltechAUTHORS:20210716-225824511
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210716-225824511
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109896
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:16 Jul 2021 23:15
Last Modified:16 Jul 2021 23:15

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