Notes on data-driven output-feedback control of linear MIMO systems
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910747853848576 |
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| author | Alsalti, Mohammad Lopez, Victor G. Müller, Matthias A. |
| author_facet | Alsalti, Mohammad Lopez, Victor G. Müller, Matthias A. |
| contents | Recent works have approached the data-driven design of dynamic output-feedback controllers for discrete-time LTI systems by constructing non-minimal state vectors composed of past inputs and outputs. Depending on the system's complexity (order $n$, lag $\ell$ and number of outputs $p$), it was observed in several works that such an approach presents significant limitations. In particular, many works require to restrict the class of LTI systems to those satisfying the relation $p\ell=n$. In this note, we show how to address the general MIMO case (for which $p\ell\geq n$ in general) by constructing an alternative non-minimal state vector from data. Different from the existing literature, our method guarantees the satisfaction of certain rank conditions when the system is persistently excited, thereby facilitating the direct data-driven dynamic output-feedback control of MIMO systems by applying methods that were originally developed for the input-state data setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_17484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Notes on data-driven output-feedback control of linear MIMO systems Alsalti, Mohammad Lopez, Victor G. Müller, Matthias A. Systems and Control Optimization and Control Recent works have approached the data-driven design of dynamic output-feedback controllers for discrete-time LTI systems by constructing non-minimal state vectors composed of past inputs and outputs. Depending on the system's complexity (order $n$, lag $\ell$ and number of outputs $p$), it was observed in several works that such an approach presents significant limitations. In particular, many works require to restrict the class of LTI systems to those satisfying the relation $p\ell=n$. In this note, we show how to address the general MIMO case (for which $p\ell\geq n$ in general) by constructing an alternative non-minimal state vector from data. Different from the existing literature, our method guarantees the satisfaction of certain rank conditions when the system is persistently excited, thereby facilitating the direct data-driven dynamic output-feedback control of MIMO systems by applying methods that were originally developed for the input-state data setting. |
| title | Notes on data-driven output-feedback control of linear MIMO systems |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2311.17484 |