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arXiv · 2505.03346

Data-Enabled Predictive Control for Nonlinear Systems Based on a Koopman Bilinear Realization

Zuxun Xiong·Zhenyi Yuan·Keyan Miao·Han Wang·Jorge Cortes·Antonis Papachristodoulou
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Abstract

This paper extends the Willems' Fundamental Lemma to nonlinear control-affine systems using the Koopman bilinear realization. This enables us to bypass the Extended Dynamic Mode Decomposition (EDMD)-based system identification step in conventional Koopman-based methods and design controllers for nonlinear systems directly from data. Leveraging this result, we develop a Data-Enabled Predictive Control (DeePC) framework for nonlinear systems with unknown dynamics. A case study demonstrates that our direct data-driven control method achieves improved optimality compared to conventional Koopman-based methods. Furthermore, in examples where an exact Koopman realization with a finite-dimensional lifting function set of the controlled nonlinear system does not exist, our method exhibits advanced robustness to finite Koopman approximation errors compared to existing methods.

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Zuxun Xiong, Zhenyi Yuan, Keyan Miao, Han Wang, Jorge Cortes, Antonis Papachristodoulou. 2025-05-06. Data-Enabled Predictive Control for Nonlinear Systems Based on a Koopman Bilinear Realization. https://arxiv.org/abs/2505.03346

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