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arXiv · 2508.11533

Integrating Uncertainties for Koopman-Based Stabilization

Yicheng Lin·Bingxian Wu·Nan Bai·Zhiyong Sun·Yunxiao Ren·Chuanze Chen·Zhisheng Duan
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Abstract

Over the past decades, the Koopman operator has been widely applied in data-driven control, yet its theoretical foundations remain underexplored. This paper establishes a unified framework to address the robust stabilization problem in data-driven control via the Koopman operator, fully accounting for three uncertainties: projection error, estimation error, and process disturbance. It comprehensively investigates both direct and indirect data-driven control approaches, facilitating flexible methodology selection for analysis and control. For the direct approach, considering process disturbances, the lifted-state feedback controller, designed via a linear matrix inequality (LMI), robustly stabilizes all lifted bilinear systems consistent with noisy data. For the indirect approach requiring system identification, the feedback controller, designed using a nonlinear matrix inequality convertible to an LMI, ensures closed-loop stability under worst-case process disturbances. Numerical simulations via cross-validation validate the effectiveness of both approaches, highlighting their theoretical significance and practical utility.

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Yicheng Lin, Bingxian Wu, Nan Bai, Zhiyong Sun, Yunxiao Ren, Chuanze Chen, Zhisheng Duan. 2025-08-15. Integrating Uncertainties for Koopman-Based Stabilization. https://arxiv.org/abs/2508.11533

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