Learning-based rigid tube model predictive control

Yulong Gao, Shuhao Yan, Jian Zhou, Mark Cannon, Alessandro Abate, Karl Henrik Johansson
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:492-503, 2024.

Abstract

This paper is concerned with model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and mixed constraints on the state and input, whereas the true disturbance set is unknown. Unlike most existing work on robust MPC, we propose an algorithm incorporating online learning that builds on prior knowledge of the disturbance, i.e., a known but conservative disturbance set. We approximate the true disturbance set at each time step with a parameterised set, which is referred to as a quantified disturbance set, using disturbance realisations. A key novelty is that the parameterisation of these quantified disturbance sets enjoys desirable properties such that the quantified disturbance set and its corresponding rigid tube bounding disturbance propagation can be efficiently updated online. We provide statistical gaps between the true and quantified disturbance sets, based on which, probabilistic recursive feasibility of MPC optimisation problems is discussed. Numerical simulations are provided to demonstrate the efficacy and computational advantages of our proposed algorithm and compare with conventional robust MPC algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-gao24a, title = {Learning-based rigid tube model predictive control}, author = {Gao, Yulong and Yan, Shuhao and Zhou, Jian and Cannon, Mark and Abate, Alessandro and Johansson, Karl Henrik}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {492--503}, 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/gao24a/gao24a.pdf}, url = {https://proceedings.mlr.press/v242/gao24a.html}, abstract = {This paper is concerned with model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and mixed constraints on the state and input, whereas the true disturbance set is unknown. Unlike most existing work on robust MPC, we propose an algorithm incorporating online learning that builds on prior knowledge of the disturbance, i.e., a known but conservative disturbance set. We approximate the true disturbance set at each time step with a parameterised set, which is referred to as a quantified disturbance set, using disturbance realisations. A key novelty is that the parameterisation of these quantified disturbance sets enjoys desirable properties such that the quantified disturbance set and its corresponding rigid tube bounding disturbance propagation can be efficiently updated online. We provide statistical gaps between the true and quantified disturbance sets, based on which, probabilistic recursive feasibility of MPC optimisation problems is discussed. Numerical simulations are provided to demonstrate the efficacy and computational advantages of our proposed algorithm and compare with conventional robust MPC algorithms.} }
Endnote
%0 Conference Paper %T Learning-based rigid tube model predictive control %A Yulong Gao %A Shuhao Yan %A Jian Zhou %A Mark Cannon %A Alessandro Abate %A Karl Henrik Johansson %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-gao24a %I PMLR %P 492--503 %U https://proceedings.mlr.press/v242/gao24a.html %V 242 %X This paper is concerned with model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and mixed constraints on the state and input, whereas the true disturbance set is unknown. Unlike most existing work on robust MPC, we propose an algorithm incorporating online learning that builds on prior knowledge of the disturbance, i.e., a known but conservative disturbance set. We approximate the true disturbance set at each time step with a parameterised set, which is referred to as a quantified disturbance set, using disturbance realisations. A key novelty is that the parameterisation of these quantified disturbance sets enjoys desirable properties such that the quantified disturbance set and its corresponding rigid tube bounding disturbance propagation can be efficiently updated online. We provide statistical gaps between the true and quantified disturbance sets, based on which, probabilistic recursive feasibility of MPC optimisation problems is discussed. Numerical simulations are provided to demonstrate the efficacy and computational advantages of our proposed algorithm and compare with conventional robust MPC algorithms.
APA
Gao, Y., Yan, S., Zhou, J., Cannon, M., Abate, A. & Johansson, K.H.. (2024). Learning-based rigid tube model predictive control. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:492-503 Available from https://proceedings.mlr.press/v242/gao24a.html.

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