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A Finite Dimensional Control of the Dynamics of the Generalized Korteweg-de Vries Burgers Equation |
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PP: 207-221 |
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Author(s) |
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Nejib Smaoui,
Mohamed Zribi,
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Abstract |
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| The paper deals with the finite dimensional control of the generalized Kortewegde
Vries Burgers (GKdVB) partial differential equation (PDE). A Karhunen-Lo`eve
Galerkin projection procedure is used to derive a system of ordinary differential equations
(ODEs) that mimics the dynamics of the GKdVB equation. Using Lyapunov
theory, it is shown that the highly nonlinear system of ODEs is stable. However, the
simulation results indicate that the system of ODEs converges slowly to the origin.
Therefore, two control schemes are proposed for the system of ODEs; the main objective
of the controllers is to speed up the convergence to the origin. The first controller
is a linear state feedback controller whereas the second controller is a nonlinear controller.
It is proven that both controllers guarantee the asymptotic convergence of the
states of the system of ODEs to zero. Simulation results indicate that the proposed
control schemes work well. |
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