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Nonlinear boundary control of the unforced generalized Korteweg–de Vries–Burgers equation

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Abstract

In this paper, we consider the boundary control problem of the unforced generalized Korteweg–de Vries–Burgers (GKdVB) equation when the spatial domain is [0,1]. Three control laws are derived for this equation and the L 2-global exponential stability of the solution is proved analytically. Numerical results using the finite element method (FEM) are presented to illustrate the developed control schemes.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Kuwait University, PO Box 5969, Safat, 13060, Kuwait

    Nejib Smaoui & Alaa El-Kadri

  2. Department of Electrical Engineering, Kuwait University, PO Box 5969, Safat, 13060, Kuwait

    Mohamed Zribi

Authors
  1. Nejib Smaoui
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  2. Alaa El-Kadri
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  3. Mohamed Zribi
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Correspondence to Nejib Smaoui.

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Smaoui, N., El-Kadri, A. & Zribi, M. Nonlinear boundary control of the unforced generalized Korteweg–de Vries–Burgers equation. Nonlinear Dyn 60, 561–574 (2010). https://doi.org/10.1007/s11071-009-9615-8

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  • DOI: https://doi.org/10.1007/s11071-009-9615-8

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