Integrating Uncertainties for Koopman-Based Stabilization
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916901485019136 |
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| author | Lin, Yicheng Wu, Bingxian Bai, Nan Sun, Zhiyong Ren, Yunxiao Chen, Chuanze Duan, Zhisheng |
| author_facet | Lin, Yicheng Wu, Bingxian Bai, Nan Sun, Zhiyong Ren, Yunxiao Chen, Chuanze Duan, Zhisheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrating Uncertainties for Koopman-Based Stabilization Lin, Yicheng Wu, Bingxian Bai, Nan Sun, Zhiyong Ren, Yunxiao Chen, Chuanze Duan, Zhisheng Systems and Control Optimization and Control 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. |
| title | Integrating Uncertainties for Koopman-Based Stabilization |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2508.11533 |