Stabilization of a one-dimensional dam-river system

Nondissipative and noncollocated case

B. Chentouf, J. M. Wang

Research output: Contribution to journalArticle

11 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

Fingerprint

Closed loop systems
Dams
Stabilization
Rivers
Unsteady flow
Wave equations
Asymptotic stability
Closed-loop System
Actuators
Hydraulics
Output Regulation
Analytic Semigroup
Riesz Basis
Shooting Method
Boundary Control
Sensors
Computer simulation
Shallow Water
Unsteady Flow
Exponential Stability

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

Cite this

Stabilization of a one-dimensional dam-river system : Nondissipative and noncollocated case. / Chentouf, B.; Wang, J. M.

In: Journal of Optimization Theory and Applications, Vol. 134, No. 2, 08.2007, p. 223-239.

Research output: Contribution to journalArticle

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