Direct data-driven stabilization of nonlinear affine systems via the Koopman operator

In this work, we are concerned with the design of direct data-driven controllers for nonlinear affine systems without explicit dynamical models. To this end, we adopt the Koopman operator to approximately reformulate the nonlinear systems into bilinear forms, based on which we propose a "simple...

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Bibliographic Details
Main Authors: Fu, Xingyun, You, Keyou
Format: Conference Proceeding
Language:English
Subjects:
Closed loop systems
Data models
Dictionaries
Nonlinear dynamical systems
Numerical stability
Robustness
Stability analysis
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Summary:In this work, we are concerned with the design of direct data-driven controllers for nonlinear affine systems without explicit dynamical models. To this end, we adopt the Koopman operator to approximately reformulate the nonlinear systems into bilinear forms, based on which we propose a "simple" static controller in the linear form of the preset function dictionary. Then, we show how to obtain the feedback gain matrix and establish the stability condition of the closed-loop system using only the off-line collected data. Finally, numerical results demonstrate the effectiveness and robustness of this data-driven controller.
ISSN:2576-2370
DOI:10.1109/CDC51059.2022.9993302