English

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

Analysis of PDEs 2017-02-24 v1

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.

Keywords

Cite

@article{arxiv.1702.07228,
  title  = {Asymptotic analysis of a 2D overhead crane with input delays in the boundary control},
  author = {Fadhel Al-Musallam and Kaïs Ammari and Boumdiène Chentouf},
  journal= {arXiv preprint arXiv:1702.07228},
  year   = {2017}
}