期刊
AUTOMATICA
卷 137, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2021.110114
关键词
Model predictive control; Koopman operators; Nonlinear systems; Robustness; Convergence
资金
- National Natural Science Foundation of China [61825305, 62003361]
- National Key R&D Program of China [2018YFB1305105]
- HUAWEI
This paper presents a robust tube-based MPC solution with Koopman operators for nonlinear discrete-time dynamical systems. The proposed approach does not assume the convergence of the approximated Koopman operator.
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. (C) 2021 Elsevier Ltd. All rights reserved.
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