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

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.
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Submitted on : Monday, July 1, 2019 - 11:36:52 AM
Last modification on : Thursday, July 18, 2019 - 2:56:10 PM

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Fadhel Al-Musallam, Kaïs Ammari, Boumediene Chentouf. Asymptotic behavior of a 2D overhead crane with input delays in the boundary control. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley-VCH Verlag, 2018, 98 (7), pp.1103-1122. ⟨10.1002/zamm.201700208⟩. ⟨hal-02169455⟩

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