Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States
It is well known that for flat systems, the tracking control problem can be solved by utilizing a linearizing quasi-static feedback of generalized states. If measurements (or estimates) of a so-called generalized Brunovský state are available, a linear, decoupled, and asymptotically stable tracking...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212349 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States. Conrad Gstöttner, Bernd Kolar and Markus Schöberl. SIGMA 20 (2024), 071, 27 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862617424121036800 |
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| author | Gstöttner, Conrad Kolar, Bernd Schöberl, Markus |
| author_facet | Gstöttner, Conrad Kolar, Bernd Schöberl, Markus |
| citation_txt | Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States. Conrad Gstöttner, Bernd Kolar and Markus Schöberl. SIGMA 20 (2024), 071, 27 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | It is well known that for flat systems, the tracking control problem can be solved by utilizing a linearizing quasi-static feedback of generalized states. If measurements (or estimates) of a so-called generalized Brunovský state are available, a linear, decoupled, and asymptotically stable tracking error dynamics can be achieved. However, from a practical point of view, it is often desirable to achieve the same tracking error dynamics by feedback of a classical state instead of a generalized one. This is due to the fact that the components of a classical state typically correspond to measurable physical quantities, whereas a generalized Brunovský state often contains higher-order time derivatives of the (fictitious) flat output, which are not directly accessible by measurements. In this paper, a systematic solution for the tracking control problem based on quasi-static feedback and measurements of classical states only is derived for the subclass of (, )-flat systems.
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| first_indexed | 2026-03-14T10:08:05Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212349 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T10:08:05Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gstöttner, Conrad Kolar, Bernd Schöberl, Markus 2026-02-05T09:55:22Z 2024 Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States. Conrad Gstöttner, Bernd Kolar and Markus Schöberl. SIGMA 20 (2024), 071, 27 pages 1815-0659 2020 Mathematics Subject Classification: 53Z30; 93C10; 93C15 arXiv:2110.12995 https://nasplib.isofts.kiev.ua/handle/123456789/212349 https://doi.org/10.3842/SIGMA.2024.071 It is well known that for flat systems, the tracking control problem can be solved by utilizing a linearizing quasi-static feedback of generalized states. If measurements (or estimates) of a so-called generalized Brunovský state are available, a linear, decoupled, and asymptotically stable tracking error dynamics can be achieved. However, from a practical point of view, it is often desirable to achieve the same tracking error dynamics by feedback of a classical state instead of a generalized one. This is due to the fact that the components of a classical state typically correspond to measurable physical quantities, whereas a generalized Brunovský state often contains higher-order time derivatives of the (fictitious) flat output, which are not directly accessible by measurements. In this paper, a systematic solution for the tracking control problem based on quasi-static feedback and measurements of classical states only is derived for the subclass of (, )-flat systems. This research was funded in whole or in part by the Austrian Science Fund (FWF) P32151 and P36473. The authors would also like to thank J. Rudolph and A. Irscheid for interesting discussions regarding the exact linearization of generalized states by quasi-static feedback. Furthermore, we would like to thank the anonymous referees whose detailed reviews helped to improve the final version of the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States Article published earlier |
| spellingShingle | Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States Gstöttner, Conrad Kolar, Bernd Schöberl, Markus |
| title | Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States |
| title_full | Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States |
| title_fullStr | Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States |
| title_full_unstemmed | Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States |
| title_short | Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States |
| title_sort | tracking control for (, )-flat systems by quasi-static feedback of classical states |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212349 |
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