Robust tube-based model predictive control with Koopman operators

Xinglong Zhang, Wei Pan, Riccardo Scattolini, Shuyou Yu, Xin Xu*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.

Original languageEnglish
Article number110114
Number of pages10
JournalAutomatica
Volume137
DOIs
Publication statusPublished - 2022

Keywords

  • Convergence
  • Koopman operators
  • Model predictive control
  • Nonlinear systems
  • Robustness

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