Efficient algorithm to solve optimal boundary control problem for Burgers' equation

Alaeddin Malek; Roghayeh Ebrahim Nataj; Mohamad Javad Yazdanpanah

Kybernetika (2012)

  • Volume: 48, Issue: 6, page 1250-1265
  • ISSN: 0023-5954

Abstract

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In this paper, we propose a novel algorithm for solving an optimal boundary control problem of the Burgers' equation. The solving method is based on the transformation of the original problem into a homogeneous boundary conditions problem. This transforms the original problem into an optimal distributed control problem. The modal expansion technique is applied to the distributed control problem of the Burgers' equation to generate a low-dimensional dynamical system. The control parametrization method is formulated for approximating the time-varying control by a finite term of the orthogonal functions with unknown coefficients determined through an optimization process. The minimization of the objective functional is performed by using a conjugate gradient method. The accuracy and convergent rate of this hybrid method are shown by some numerical examples .

How to cite

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Malek, Alaeddin, Nataj, Roghayeh Ebrahim, and Yazdanpanah, Mohamad Javad. "Efficient algorithm to solve optimal boundary control problem for Burgers' equation." Kybernetika 48.6 (2012): 1250-1265. <http://eudml.org/doc/251389>.

@article{Malek2012,
abstract = {In this paper, we propose a novel algorithm for solving an optimal boundary control problem of the Burgers' equation. The solving method is based on the transformation of the original problem into a homogeneous boundary conditions problem. This transforms the original problem into an optimal distributed control problem. The modal expansion technique is applied to the distributed control problem of the Burgers' equation to generate a low-dimensional dynamical system. The control parametrization method is formulated for approximating the time-varying control by a finite term of the orthogonal functions with unknown coefficients determined through an optimization process. The minimization of the objective functional is performed by using a conjugate gradient method. The accuracy and convergent rate of this hybrid method are shown by some numerical examples .},
author = {Malek, Alaeddin, Nataj, Roghayeh Ebrahim, Yazdanpanah, Mohamad Javad},
journal = {Kybernetika},
keywords = {optimal boundary control; Burgers' equation; conjugate gradient method; modal expansion technique; control parametrization; optimal boundary control; Burgers' equation; conjugate gradient method; modal expansion technique; control parametrization},
language = {eng},
number = {6},
pages = {1250-1265},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Efficient algorithm to solve optimal boundary control problem for Burgers' equation},
url = {http://eudml.org/doc/251389},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Malek, Alaeddin
AU - Nataj, Roghayeh Ebrahim
AU - Yazdanpanah, Mohamad Javad
TI - Efficient algorithm to solve optimal boundary control problem for Burgers' equation
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 6
SP - 1250
EP - 1265
AB - In this paper, we propose a novel algorithm for solving an optimal boundary control problem of the Burgers' equation. The solving method is based on the transformation of the original problem into a homogeneous boundary conditions problem. This transforms the original problem into an optimal distributed control problem. The modal expansion technique is applied to the distributed control problem of the Burgers' equation to generate a low-dimensional dynamical system. The control parametrization method is formulated for approximating the time-varying control by a finite term of the orthogonal functions with unknown coefficients determined through an optimization process. The minimization of the objective functional is performed by using a conjugate gradient method. The accuracy and convergent rate of this hybrid method are shown by some numerical examples .
LA - eng
KW - optimal boundary control; Burgers' equation; conjugate gradient method; modal expansion technique; control parametrization; optimal boundary control; Burgers' equation; conjugate gradient method; modal expansion technique; control parametrization
UR - http://eudml.org/doc/251389
ER -

References

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