Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates

Liang Wu, Wallace Gian Yion Tan, Richard Braatz, Jan Drgona
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1791-1803, 2026.

Abstract

At present, solving large-scale nonlinear model predictive control (NMPC) problems at kilohertz (kHz) rates on standard processors remains a formidable challenge. This paper proposes a Koopman-BoxQP framework that i) learns a linear Koopman high-dimensional model, ii) eliminates the high-dimensional observables to get the multi-step prediction model of the states and control inputs, iii) penalizes the multi-step prediction model into the objective, which results in a structured box-constrained quadratic program (BoxQP) whose decision variables include both the system states and control inputs, iv) develops a structure-exploited and warm-starting-supported variant of feasible Mehrotra’s interior-point algorithm for BoxQP. Numerical results demonstrate that Koopman-BoxQP can solve a large-scale NMPC problem with 1040 variables and 2080 inequalities at a kHz rate.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-wu26a, title = {Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates}, author = {Wu, Liang and Tan, Wallace Gian Yion and Braatz, Richard and Drgona, Jan}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1791--1803}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/wu26a/wu26a.pdf}, url = {https://proceedings.mlr.press/v331/wu26a.html}, abstract = {At present, solving large-scale nonlinear model predictive control (NMPC) problems at kilohertz (kHz) rates on standard processors remains a formidable challenge. This paper proposes a Koopman-BoxQP framework that i) learns a linear Koopman high-dimensional model, ii) eliminates the high-dimensional observables to get the multi-step prediction model of the states and control inputs, iii) penalizes the multi-step prediction model into the objective, which results in a structured box-constrained quadratic program (BoxQP) whose decision variables include both the system states and control inputs, iv) develops a structure-exploited and warm-starting-supported variant of feasible Mehrotra’s interior-point algorithm for BoxQP. Numerical results demonstrate that Koopman-BoxQP can solve a large-scale NMPC problem with 1040 variables and 2080 inequalities at a kHz rate.} }
Endnote
%0 Conference Paper %T Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates %A Liang Wu %A Wallace Gian Yion Tan %A Richard Braatz %A Jan Drgona %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-wu26a %I PMLR %P 1791--1803 %U https://proceedings.mlr.press/v331/wu26a.html %V 331 %X At present, solving large-scale nonlinear model predictive control (NMPC) problems at kilohertz (kHz) rates on standard processors remains a formidable challenge. This paper proposes a Koopman-BoxQP framework that i) learns a linear Koopman high-dimensional model, ii) eliminates the high-dimensional observables to get the multi-step prediction model of the states and control inputs, iii) penalizes the multi-step prediction model into the objective, which results in a structured box-constrained quadratic program (BoxQP) whose decision variables include both the system states and control inputs, iv) develops a structure-exploited and warm-starting-supported variant of feasible Mehrotra’s interior-point algorithm for BoxQP. Numerical results demonstrate that Koopman-BoxQP can solve a large-scale NMPC problem with 1040 variables and 2080 inequalities at a kHz rate.
APA
Wu, L., Tan, W.G.Y., Braatz, R. & Drgona, J.. (2026). Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1791-1803 Available from https://proceedings.mlr.press/v331/wu26a.html.

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