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Adomian method for solving adaptive control problem

S. Manseur (Department of Mathematics, University of Blida, Blida, Algeria)
Y. Cherruault (MEDIMAT Laboratory, University Paris VI, Paris, France)

Kybernetes

ISSN: 0368-492X

Article publication date: 1 August 2005

434

Abstract

Purpose

Aims to propose methodology to solve adaptive control problems by the use of the Adomian decomposition method (ADM).

Design/methodology/approach

The approach to this problem is through the ADM which consists in finding a solution of nonlinear state equations as a convergent series that depends on the unknown parameters of the system.

Findings

It was shown that a first approach for solving adaptive control problems could be tackled by using the ADM. The solution of the systems was obtained in a series forms as a function of the unknown parameters. The objective function became a function that explicitly depends on parameters. This, it was shown, can be minimised by classical or nonclassical global optimization methods.

Research limitations/implications

The methods presented depends on ADM. It is proposed that future work involves the study of an adaptive control problem associated to a nonlinear compartmental systems of Michaels‐Menten type.

Originality/value

Presents an applications of the developed ADM using it, as adapted to control problems. It contributes to mathematical modelling studied concerning most biological, physical phenomena which are described by nonlinear systems: differential, partial differential in form and for which there is little hope of finding an exact solution.

Keywords

Citation

Manseur, S. and Cherruault, Y. (2005), "Adomian method for solving adaptive control problem", Kybernetes, Vol. 34 No. 7/8, pp. 992-998. https://doi.org/10.1108/03684920510605812

Publisher

:

Emerald Group Publishing Limited

Copyright © 2005, Emerald Group Publishing Limited

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