Learning-based robust model predictive control with data-driven Koopman operators

doi:10.1007/s13042-023-01834-5

2023-04-23

PRE

Meixi Wang

Xuyang Lou *

Baotong Cui

DOI：10.1007/s13042-023-01834-5

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摘要

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This paper presents a data-driven control strategy for nonlinear dynamical systems, which fully exploits the advantages of the Koopman operator in globally linearizing nonlinear dynamical systems. We first generalize the Koopman operator framework to the controlled nonlinear systems, enabling comprehensive linear analysis and control methods to be valid for nonlinear systems. When extracting the Koopman operator approximation from data, model uncertainty always arises due to the variation of the data-driven setting. We next present a hierarchical neural network (HNN) approach to approximate the finite-dimensional Koopman operator representations and construct multiple Koopman-based lifted models for original controlled nonlinear systems in a polytope set construction. Based on that, a robust Koopman-based model predictive control (rKMPC) approach considering state and input constraints is constructed to realize the control of the original nonlinear systems. In particular, we extend the proposed rKMPC framework to a Koopman operator-based reduced-order model, thereby achieving the nonlinear control using only a few given inputs. Finally, several numerical examples and a physical experiment are provided to demonstrate the effectiveness of the proposed data-driven control approach, and numerical comparisons are carried out with existing Koopman-based control methods.

Keyword:

Koopman operator

Hierarchical neural network

Data-driven control

Model predictive control

Nonlinear dynamical system