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.

Robust tube-based model predictive control with Koopman operators

Zhang X.;Scattolini R.;
2022

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.
File in questo prodotto:
File Dimensione Formato  
Koopman_Automatica.pdf

accesso aperto

: Pre-Print (o Pre-Refereeing)
Dimensione 2.78 MB
Formato Adobe PDF
2.78 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1199433
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? ND
social impact