Stability analysis and numerical simulations of a one dimensional open channel hydraulic system

Boumediène Chentouf*, Nejib Smaoui

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in a functional space. Furthermore, the spectrum and resolvent sets of the system operator are characterized. Then, stability results are stated and proved according to a smallness assumption on the feedback gain. The proof invokes Lyapunov direct method. Last but not least, we adopt the Chebychev collocation method, that uses backward Euler method and the Gauss-Lobatto points, to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes.

Original languageEnglish
Pages (from-to)498-511
Number of pages14
JournalApplied Mathematics and Computation
Volume321
DOIs
Publication statusPublished - Mar 15 2018
Externally publishedYes

Keywords

  • Chebychev collocation method
  • Open channel hydraulic system
  • Output boundary feedback control
  • Stability

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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