Mapping back and forth between model predictive control and neural networks

Ross Drummond, Pablo Baldivieso, Giorgio Valmorbida
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:1228-1240, 2024.

Abstract

Model predictive control (MPC) for linear systems with quadratic costs and linear constraints is shown to admit an exact representation as an implicit neural network. A method to “unravel” the implicit neural network of MPC into an explicit one is also introduced. As well as building links between model-based and data-driven control, these results emphasize the capability of implicit neural networks for representing solutions of optimisation problems, as such problems are themselves implicitly defined functions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-drummond24a, title = {Mapping back and forth between model predictive control and neural networks}, author = {Drummond, Ross and Baldivieso, Pablo and Valmorbida, Giorgio}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {1228--1240}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/drummond24a/drummond24a.pdf}, url = {https://proceedings.mlr.press/v242/drummond24a.html}, abstract = {Model predictive control (MPC) for linear systems with quadratic costs and linear constraints is shown to admit an exact representation as an implicit neural network. A method to “unravel” the implicit neural network of MPC into an explicit one is also introduced. As well as building links between model-based and data-driven control, these results emphasize the capability of implicit neural networks for representing solutions of optimisation problems, as such problems are themselves implicitly defined functions.} }
Endnote
%0 Conference Paper %T Mapping back and forth between model predictive control and neural networks %A Ross Drummond %A Pablo Baldivieso %A Giorgio Valmorbida %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-drummond24a %I PMLR %P 1228--1240 %U https://proceedings.mlr.press/v242/drummond24a.html %V 242 %X Model predictive control (MPC) for linear systems with quadratic costs and linear constraints is shown to admit an exact representation as an implicit neural network. A method to “unravel” the implicit neural network of MPC into an explicit one is also introduced. As well as building links between model-based and data-driven control, these results emphasize the capability of implicit neural networks for representing solutions of optimisation problems, as such problems are themselves implicitly defined functions.
APA
Drummond, R., Baldivieso, P. & Valmorbida, G.. (2024). Mapping back and forth between model predictive control and neural networks. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:1228-1240 Available from https://proceedings.mlr.press/v242/drummond24a.html.

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