Distributed Control of the Generalized Korteweg-de Vries-Burgers Equation | Zendy

Nejib Smaoui | Zendy; Rasha H. Al-Jamal | Zendy

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Distributed Control of the Generalized Korteweg-de Vries-Burgers Equation

Author(s) -

Nejib Smaoui,

Rasha H. Al-Jamal

Publication year - 2008

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2008/621672

Subject(s) - mathematics , burgers' equation , ode , galerkin method , korteweg–de vries equation , partial differential equation , linearization , ordinary differential equation , projection (relational algebra) , nonlinear system , stability (learning theory) , mathematical analysis , differential equation , computer science , algorithm , physics , quantum mechanics , machine learning

The paper deals with the distributed control of the generalized Kortweg-de Vries-Burgers equation (GKdVB) subject to periodic boundary conditions via the Karhunen-LoÃƒÂ¨ve (K-L) Galerkin method. The decomposition procedure of the K-L method is presented to illustrate the use of this method in analyzing the numerical simulations data which represent the solutions to the GKdVB equation. The K-L Galerkin projection is used as a model reduction technique for nonlinear systems to derive a system of ordinary differential equations (ODEs) that mimics the dynamics of the GKdVB equation. The data coefficients derived from the ODE system are then used to approximate the solutions of the GKdVB equation. Finally, three state feedback linearization control schemes with the objective of enhancing the stability of the GKdVB equation are proposed. Simulations of the controlled system are given to illustrate the developed theory

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