Stabilization of a one-dimensional dam-river system: Nondissipative and noncollocated case

B. Chentouf*, J. M. Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

In this paper, we consider a one-dimensional dam-river system, described by a diffusive-wave equation and often used in hydraulic engineering to model the dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not important. We propose an integral boundary control which leads to a nondissipative closed-loop system with noncollocated actuators and sensors; hence, two main difficulties arise: first, how to show the C 0-semigroup generation and second, how to achieve the stability of the system. To overcome this situation, the Riesz basis methodology is adopted to show that the closed-loop system generates an analytic semigroup. Concerning the stability, the shooting method is applied to assign the spectrum of the system in the open left-half plane and ensure its exponential stability as well as the output regulation. Numerical simulations are presented for a family of system parameters.

Original languageEnglish
Pages (from-to)223-239
Number of pages17
JournalJournal of Optimization Theory and Applications
Volume134
Issue number2
DOIs
Publication statusPublished - Aug 2007

Keywords

  • Analytic semigroups
  • Diffusive-wave equations
  • Riesz spectral operators
  • Robust output regulation
  • Stability

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research

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