On the Exponential Stability of Koopman Model Predictive Control

Xu Shang, Jorge Cortes, Yang Zheng
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1694-1712, 2026.

Abstract

Koopman Model Predictive Control (MPC) uses a lifted linear predictor to efficiently handle constrained nonlinear systems. While constraint satisfaction and (practical) asymptotic stability have been studied, explicit guarantees of local exponential stability seem to be missing. This paper revisits the exponential stability for Koopman MPC. We first analyze a Koopman LQR problem and show that 1) with zero modeling error, the lifted LQR policy is globally optimal and globally asymptotically stabilizes the nonlinear plant, and 2) with the lifting function and one-step prediction error both Lipschitz at the origin, the closed-loop system is locally exponentially stable. These results facilitate terminal cost/set design in the lifted Koopman space. Leveraging linear-MPC properties (boundedness, value decrease, recursive feasibility), we then prove local exponential stability for a stabilizing Koopman MPC under the same conditions as Koopman LQR. Experiments on an inverted pendulum show better convergence performance and lower accumulated cost than the traditional Taylor-linearized MPC approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-shang26a, title = {On the Exponential Stability of Koopman Model Predictive Control}, author = {Shang, Xu and Cortes, Jorge and Zheng, Yang}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1694--1712}, 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/shang26a/shang26a.pdf}, url = {https://proceedings.mlr.press/v331/shang26a.html}, abstract = {Koopman Model Predictive Control (MPC) uses a lifted linear predictor to efficiently handle constrained nonlinear systems. While constraint satisfaction and (practical) asymptotic stability have been studied, explicit guarantees of local exponential stability seem to be missing. This paper revisits the exponential stability for Koopman MPC. We first analyze a Koopman LQR problem and show that 1) with zero modeling error, the lifted LQR policy is globally optimal and globally asymptotically stabilizes the nonlinear plant, and 2) with the lifting function and one-step prediction error both Lipschitz at the origin, the closed-loop system is locally exponentially stable. These results facilitate terminal cost/set design in the lifted Koopman space. Leveraging linear-MPC properties (boundedness, value decrease, recursive feasibility), we then prove local exponential stability for a stabilizing Koopman MPC under the same conditions as Koopman LQR. Experiments on an inverted pendulum show better convergence performance and lower accumulated cost than the traditional Taylor-linearized MPC approaches.} }
Endnote
%0 Conference Paper %T On the Exponential Stability of Koopman Model Predictive Control %A Xu Shang %A Jorge Cortes %A Yang Zheng %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-shang26a %I PMLR %P 1694--1712 %U https://proceedings.mlr.press/v331/shang26a.html %V 331 %X Koopman Model Predictive Control (MPC) uses a lifted linear predictor to efficiently handle constrained nonlinear systems. While constraint satisfaction and (practical) asymptotic stability have been studied, explicit guarantees of local exponential stability seem to be missing. This paper revisits the exponential stability for Koopman MPC. We first analyze a Koopman LQR problem and show that 1) with zero modeling error, the lifted LQR policy is globally optimal and globally asymptotically stabilizes the nonlinear plant, and 2) with the lifting function and one-step prediction error both Lipschitz at the origin, the closed-loop system is locally exponentially stable. These results facilitate terminal cost/set design in the lifted Koopman space. Leveraging linear-MPC properties (boundedness, value decrease, recursive feasibility), we then prove local exponential stability for a stabilizing Koopman MPC under the same conditions as Koopman LQR. Experiments on an inverted pendulum show better convergence performance and lower accumulated cost than the traditional Taylor-linearized MPC approaches.
APA
Shang, X., Cortes, J. & Zheng, Y.. (2026). On the Exponential Stability of Koopman Model Predictive Control. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1694-1712 Available from https://proceedings.mlr.press/v331/shang26a.html.

Related Material