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
Date:2024
Main Authors: Gstöttner, Conrad, Kolar, Bernd, Schöberl, Markus
Format: Article
Language:English
Published: Інститут математики НАН України 2024
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
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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.
first_indexed 2026-03-14T10:08:05Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2026-03-14T10:08:05Z
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publisher Інститут математики НАН України
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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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States
Article
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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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AT schoberlmarkus trackingcontrolforflatsystemsbyquasistaticfeedbackofclassicalstates