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arXiv · 1702.07228

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

Fadhel Al-Musallam·Kaïs Ammari·Boumdiène Chentouf
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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 facts 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 polynomial.

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Fadhel Al-Musallam, Kaïs Ammari, Boumdiène Chentouf. 2017-02-23. Asymptotic analysis of a 2D overhead crane with input delays in the boundary control. https://arxiv.org/abs/1702.07228

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