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Stabilization of a One-Dimensional Dam-River System: Nondissipative and Noncollocated Case

Author

Listed:
  • B. Chentouf

    (Sultan Qaboos University)

  • J. M. Wang

    (Beijing Institute of Technology)

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.

Suggested Citation

  • B. Chentouf & J. M. Wang, 2007. "Stabilization of a One-Dimensional Dam-River System: Nondissipative and Noncollocated Case," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 223-239, August.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:2:d:10.1007_s10957-007-9223-z
    DOI: 10.1007/s10957-007-9223-z
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    Cited by:

    1. K. Ammari & B. Chentouf, 2010. "Further Results on the Robust Regulation of a One-Dimensional Dam-River System," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 597-606, December.
    2. Mean, Sovanna & Unami, Koichi & Okamoto, Hisashi & Fujihara, Masayuki, 2022. "A thorough description of one-dimensional steady open channel flows using the notion of viscosity solution," Applied Mathematics and Computation, Elsevier, vol. 415(C).

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