Robust tube-based model predictive control with Koopman operators

Robust tube-based model predictive control with Koopman operators

Zhang, Xinglong (National University of Defense Technology)
Pan, W. (TU Delft Robot Dynamics)
Scattolini, Riccardo (Politecnico di Milano)
Yu, Shuyou (Jilin University)
Xu, Xin (National University of Defense Technology)

2022

Koopman operators are of infinite dimension and capture the characteristics of nonlinear dynamics in a lifted global linear manner. The finite data-driven approximation of Koopman operators results in a class of linear predictors, useful for formulating linear model predictive control (MPC) of nonlinear dynamical systems with reduced computational complexity. However, the robustness of the closed-loop Koopman MPC under modeling approximation errors and possible exogenous disturbances is still a crucial issue to be resolved. Aiming at the above problem, this paper presents a robust tube-based MPC solution with Koopman operators, i.e., r-KMPC, for nonlinear discrete-time dynamical systems with additive disturbances. The proposed controller is composed of a nominal MPC using a lifted Koopman model and an off-line nonlinear feedback policy. The proposed approach does not assume the convergence of the approximated Koopman operator, which allows using a Koopman model with a limited order for controller design. Fundamental properties, e.g., stabilizability, observability, of the Koopman model are derived under standard assumptions with which, the closed-loop robustness and nominal point-wise convergence are proven. Simulated examples are illustrated to verify the effectiveness of the proposed approach.

Convergence
Koopman operators
Model predictive control
Nonlinear systems
Robustness

http://resolver.tudelft.nl/uuid:b5a1ddec-2b50-449f-88a3-ab0855a8070d

https://doi.org/10.1016/j.automatica.2021.110114

2023-07-01

0005-1098

Automatica, 137

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2022 Xinglong Zhang, W. Pan, Riccardo Scattolini, Shuyou Yu, Xin Xu