Active optimal control of the KdV equation using the variational iteration method
type: Item
instance of: scholarly article
title: Active optimal control of the KdV equation using the variational iteration method
zbMATH Open document ID: 1207.35258
DOI: 10.1155/2010/929103
author: Ismail Kucuk
published in: Mathematical Problems in Engineering
publication date: 2010-09-30T00:00:00Z
full work available at URL: https://eudml.org/doc/232798
review text: Summary: The optimal pointwise control of the KdV equation is investigated with an objective of minimizing a given performance measure. The performance measure is specified as a quadratic functional of the final state and velocity functions along with the energy due to open- and closed-loop controls. The minimization of the performance measure over the controls is subjected to the KdV equation with periodic boundary conditions and appropriate initial condition. In contrast to standard optimal control or variational methods, a direct control parameterization is used in this study which presents a distinct approach toward the solution of optimal control problems. The method is based on finite terms of Fourier series approximation of each time control variable with unknown Fourier coefficients and frequencies. He's variational iteration method for the nonlinear partial differential equations is applied to the problem and thus converting the optimal control of lumped parameter systems into a mathematical programming. A numerical simulation is provided to exemplify the proposed method.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35A22
zbMATH DE Number: 5793805
zbMATH Keywords: optimal pointwise control
zbMATH Keywords: KdV equation
zbMATH Keywords: performance measure
zbMATH Keywords: direct control parametrization
Wikidata QID: Q58653426
MaRDI profile type: Publication
OpenAlex ID: W2011276065
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description: scientific article; zbMATH DE number 5793805