Optimal boundary control for hyperdiffusion equation

Hanif Heidari; Alaeddin Malek

Kybernetika (2010)

  • Volume: 46, Issue: 5, page 907-925
  • ISSN: 0023-5954

Abstract

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In this paper, we consider the solution of optimal control problem for hyperdiffusion equation involving boundary function of continuous time variable in its cost function. A specific direct approach based on infinite series of Fourier expansion in space and temporal integration by parts for analytical solution is proposed to solve optimal boundary control for hyperdiffusion equation. The time domain is divided into number of finite subdomains and optimal function is estimated at each subdomain to obtain desired state with minimum energy. Proposed method has high flexibility so that decision makers are able to trace optimal control in a prescribed subinterval. The implementation of the theory is presented and the effectiveness of the boundary control is investigated by some numerical examples.

How to cite

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Heidari, Hanif, and Malek, Alaeddin. "Optimal boundary control for hyperdiffusion equation." Kybernetika 46.5 (2010): 907-925. <http://eudml.org/doc/196455>.

@article{Heidari2010,
abstract = {In this paper, we consider the solution of optimal control problem for hyperdiffusion equation involving boundary function of continuous time variable in its cost function. A specific direct approach based on infinite series of Fourier expansion in space and temporal integration by parts for analytical solution is proposed to solve optimal boundary control for hyperdiffusion equation. The time domain is divided into number of finite subdomains and optimal function is estimated at each subdomain to obtain desired state with minimum energy. Proposed method has high flexibility so that decision makers are able to trace optimal control in a prescribed subinterval. The implementation of the theory is presented and the effectiveness of the boundary control is investigated by some numerical examples.},
author = {Heidari, Hanif, Malek, Alaeddin},
journal = {Kybernetika},
keywords = {hyperdiffusion equation; optimal boundary control; swimming at microscale; swimming at microscale; Fourier expansion in space; temporal integration by parts; numerical examples},
language = {eng},
number = {5},
pages = {907-925},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Optimal boundary control for hyperdiffusion equation},
url = {http://eudml.org/doc/196455},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Heidari, Hanif
AU - Malek, Alaeddin
TI - Optimal boundary control for hyperdiffusion equation
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 5
SP - 907
EP - 925
AB - In this paper, we consider the solution of optimal control problem for hyperdiffusion equation involving boundary function of continuous time variable in its cost function. A specific direct approach based on infinite series of Fourier expansion in space and temporal integration by parts for analytical solution is proposed to solve optimal boundary control for hyperdiffusion equation. The time domain is divided into number of finite subdomains and optimal function is estimated at each subdomain to obtain desired state with minimum energy. Proposed method has high flexibility so that decision makers are able to trace optimal control in a prescribed subinterval. The implementation of the theory is presented and the effectiveness of the boundary control is investigated by some numerical examples.
LA - eng
KW - hyperdiffusion equation; optimal boundary control; swimming at microscale; swimming at microscale; Fourier expansion in space; temporal integration by parts; numerical examples
UR - http://eudml.org/doc/196455
ER -

References

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