Data-Driven Structured Controller Design Using the Matrix S-Procedure
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914362318389248 |
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| author | Yang, Zhaohua Zhong, Yuxing Yang, Nachuan Lyu, Xiaoxu Shi, Ling |
| author_facet | Yang, Zhaohua Zhong, Yuxing Yang, Nachuan Lyu, Xiaoxu Shi, Ling |
| contents | This paper focuses on the data-driven optimal structured controller design for discrete-time linear time-invariant (LTI) systems, considering both the $H_2$ performance and the $H_\infty$ performance. Specifically, we consider three scenarios: (i) the model-based structured control, (ii) the data-driven unstructured control, and (iii) the data-driven structured control. For the $H_2$ performance, we primarily investigate cases (ii) and (iii), since case (i) has been extensively studied in the literature. For the $H_\infty$ performance, all three scenarios are considered. For the structured control, we introduce a linearization technique that transforms the original nonconvex problem into a semidefinite programming (SDP) problem. Based on this transformation, we develop an iterative linear matrix inequality (ILMI) algorithm. For the data-driven control, we describe the set of all possible system matrices that can generate the sequence of collected data. Additionally, we propose a sufficient condition to handle all possible system matrices using the matrix S-procedure. The data-driven structured control is followed by combining the previous two cases. We compare our methods with those in the existing literature and demonstrate our superiority via several numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-Driven Structured Controller Design Using the Matrix S-Procedure Yang, Zhaohua Zhong, Yuxing Yang, Nachuan Lyu, Xiaoxu Shi, Ling Optimization and Control This paper focuses on the data-driven optimal structured controller design for discrete-time linear time-invariant (LTI) systems, considering both the $H_2$ performance and the $H_\infty$ performance. Specifically, we consider three scenarios: (i) the model-based structured control, (ii) the data-driven unstructured control, and (iii) the data-driven structured control. For the $H_2$ performance, we primarily investigate cases (ii) and (iii), since case (i) has been extensively studied in the literature. For the $H_\infty$ performance, all three scenarios are considered. For the structured control, we introduce a linearization technique that transforms the original nonconvex problem into a semidefinite programming (SDP) problem. Based on this transformation, we develop an iterative linear matrix inequality (ILMI) algorithm. For the data-driven control, we describe the set of all possible system matrices that can generate the sequence of collected data. Additionally, we propose a sufficient condition to handle all possible system matrices using the matrix S-procedure. The data-driven structured control is followed by combining the previous two cases. We compare our methods with those in the existing literature and demonstrate our superiority via several numerical simulations. |
| title | Data-Driven Structured Controller Design Using the Matrix S-Procedure |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.14949 |