Asymptotic behavior of a 2D overhead crane with input delays in the boundary control

Fadhel Al-Musallam; Kaïs Ammari; Boumediene Chentouf

Asymptotic behavior of a 2D overhead crane with input delays in the boundary control

Fadhel Al-Musallam ¹ Kaïs Ammari ^{2, 3} Boumediene Chentouf

2 FSM - Faculté des Sciences de Monastir

3 LMV - Laboratoire de Mathématiques de Versailles

Abstract : The paper investigates the asymptotic behavior of a 2D overhead crane with input delays in the boundary control. A linear boundary control is proposed. The main feature of such a control lies in the fact that it solely depends on the velocity but under the presence of time-delays. We end-up with a closed-loop system where no displacement term is involved. It is shown that the problem is well-posed in the sense of semigroups theory. LaSalle's invariance principle is invoked in order to establish the asymptotic convergence for the solutions of the system to a stationary position which depends on the initial data. Using a resolvent method, it is proved that the convergence is indeed of polynomial type as long as the delay term satisfies a smallness condition. Lastly, non-convergence results are put forward in the case when such a condition on the delay term is not fulfilled.

Keywords : polynomial convergence asymptotic behavior boundary velocity control overhead crane time-delay

Document type :

Journal articles

Domain :

Mathematics [math]

Complete list of metadatas

https://hal.uvsq.fr/hal-02169455
Contributor : Équipe Hal Uvsq <>
Submitted on : Monday, July 1, 2019 - 11:36:52 AM
Last modification on : Thursday, July 18, 2019 - 2:56:10 PM

Asymptotic behavior of a 2D overhead crane with input delays in the boundary control

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Asymptotic behavior of a 2D overhead crane with input delays in the boundary control

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