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International Journal of Control Volume 93, 2020 - Issue 6
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On simple scheme of finite/fixed-time control designFootnote*

Konstantin ZimenkoDepartment of Control Systems and Informatics, ITMO University, Saint Petersburg, RussiaCorrespondence[email protected]
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Andrey PolyakovDepartment of Control Systems and Informatics, ITMO University, Saint Petersburg, Russia;Non-A INRIA – LNE, Villeneuve d'Ascq, France;CRIStAL (UMR-CNRS 9189), Villeneuve-d'Ascq, FranceView further author information
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Denis EfimovDepartment of Control Systems and Informatics, ITMO University, Saint Petersburg, Russia;Non-A INRIA – LNE, Villeneuve d'Ascq, France;CRIStAL (UMR-CNRS 9189), Villeneuve-d'Ascq, FranceORCID Iconhttps://orcid.org/0000-0001-8847-5235View further author information
ORCID Icon &
Wilfrid PerruquettiNon-A INRIA – LNE, Villeneuve d'Ascq, France;CRIStAL (UMR-CNRS 9189), Villeneuve-d'Ascq, FranceView further author information
Pages 1353-1361 | Received 16 Jan 2018, Accepted 23 Jul 2018, Published online: 13 Aug 2018
 
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ABSTRACT

Control laws are designed for stabilisation of a chain of integrators of arbitrary degree in finite and fixed time. Presented control laws are obtained with use of Lyapunov function method and homogeneity concept. The present analysis is based on use of explicitly defined Lyapunov function that is the hallmark with respect to similar works. This analysis allows to get simple procedure of parameters tuning and obtain new estimates for settling-time function. The theoretical results are supported by numerical examples.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

* A preliminary version of this work (Zimenko, Polyakov, Efimov, & Perruquetti, Citation2018) does not contain proofs and the case of continuous fixed-time control design.

Additional information

Funding

This work is supported by the Russian Science Foundation under grant 17-19-01422.

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