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IMA Journal of Mathematical Control and Information Advance Access published online on October 26, 2005
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dni060
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received August 11, 2004
Accepted March 11, 2005

Article

Sliding mode control of the forced generalized Burgers equation

Nejib Smaoui 1*, Mohamed Zribi 2, and Abdulla Almulla 1

1 Department of Mathematics and Computer Science, Kuwait University, PO Box 5969, Safat 13060, Kuwait
2 Department of Electrical Engineering, Kuwait University, PO Box 5969, Safat 13060, Kuwait

* To whom correspondence should be addressed.
Nejib Smaoui, E-mail: smaoui{at}mcs.sci.kuniv.edu.kw


  Abstract

This paper deals with the sliding mode control (SMC) of the forced generalized Burgers equation via the Karhunen-Loève (K-L) Galerkin method. The decomposition procedure of the K-L method is presented to illustrate the use of this method in analysing the numerical simulations data which represent the solutions of the forced generalized Burgers equation for viscosity ranging from 1 to 100. The K-L Galerkin projection is used as a model reduction technique for non-linear systems to derive a system of ordinary differential equations (ODEs) that mimics the dynamics of the forced generalized Burgers equation. The data coefficients derived from the ODE system are then used to approximate the solutions of the forced Burgers equation. Finally, static and dynamic SMC schemes with the objective of enhancing the stability of the forced generalized Burgers equation are proposed. Simulations of the controlled system are given to illustrate the developed theory.

Keywords: distributed control; generalized Burgers equation; Karhunen-Loéve decomposition.
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