{"ID":2881997,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.11533","arxiv_id":"2508.11533","title":"Integrating Uncertainties for Koopman-Based Stabilization","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.","short_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 uncertainti...","url_abs":"https://arxiv.org/abs/2508.11533","url_pdf":"https://arxiv.org/pdf/2508.11533v1","authors":"[\"Yicheng Lin\",\"Bingxian Wu\",\"Nan Bai\",\"Zhiyong Sun\",\"Yunxiao Ren\",\"Chuanze Chen\",\"Zhisheng Duan\"]","published":"2025-08-15T15:20:48Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}