Optimal control solution for Pennes' equation using strongly continuous semigroup

Alaeddin Malek; Ghasem Abbasi

Kybernetika (2014)

  • Volume: 50, Issue: 4, page 530-543
  • ISSN: 0023-5954

Abstract

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A distributed optimal control problem on and inside a homogeneous skin tissue is solved subject to Pennes' equation with Dirichlet boundary condition at one end and Rubin condition at the other end. The point heating power induced by conducting heating probe inserted at the tumour site as an unknown control function at specific depth inside biological body is preassigned. Corresponding pseudo-port Hamiltonian system is proposed. Moreover, it is proved that bioheat transfer equation forms a contraction and dissipative system. Mild solution for bioheat transfer equation and its adjoint problem are proposed. Controllability and exponentially stability for the related system is proved. The optimal control problem is solved using strongly continuous semigroup solution and time discretization. Mathematical simulations for a thermal therapy in the presence of point heating power are presented to investigate efficiency of the proposed technique.

How to cite

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Malek, Alaeddin, and Abbasi, Ghasem. "Optimal control solution for Pennes' equation using strongly continuous semigroup." Kybernetika 50.4 (2014): 530-543. <http://eudml.org/doc/262004>.

@article{Malek2014,
abstract = {A distributed optimal control problem on and inside a homogeneous skin tissue is solved subject to Pennes' equation with Dirichlet boundary condition at one end and Rubin condition at the other end. The point heating power induced by conducting heating probe inserted at the tumour site as an unknown control function at specific depth inside biological body is preassigned. Corresponding pseudo-port Hamiltonian system is proposed. Moreover, it is proved that bioheat transfer equation forms a contraction and dissipative system. Mild solution for bioheat transfer equation and its adjoint problem are proposed. Controllability and exponentially stability for the related system is proved. The optimal control problem is solved using strongly continuous semigroup solution and time discretization. Mathematical simulations for a thermal therapy in the presence of point heating power are presented to investigate efficiency of the proposed technique.},
author = {Malek, Alaeddin, Abbasi, Ghasem},
journal = {Kybernetika},
keywords = {optimal control; Pennes' bioheat equation; semigroup theory; thermal therapy; hyperthermia; optimal control; Pennes' bioheat equation; semigroup theory; thermal therapy; hyperthermia},
language = {eng},
number = {4},
pages = {530-543},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Optimal control solution for Pennes' equation using strongly continuous semigroup},
url = {http://eudml.org/doc/262004},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Malek, Alaeddin
AU - Abbasi, Ghasem
TI - Optimal control solution for Pennes' equation using strongly continuous semigroup
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 4
SP - 530
EP - 543
AB - A distributed optimal control problem on and inside a homogeneous skin tissue is solved subject to Pennes' equation with Dirichlet boundary condition at one end and Rubin condition at the other end. The point heating power induced by conducting heating probe inserted at the tumour site as an unknown control function at specific depth inside biological body is preassigned. Corresponding pseudo-port Hamiltonian system is proposed. Moreover, it is proved that bioheat transfer equation forms a contraction and dissipative system. Mild solution for bioheat transfer equation and its adjoint problem are proposed. Controllability and exponentially stability for the related system is proved. The optimal control problem is solved using strongly continuous semigroup solution and time discretization. Mathematical simulations for a thermal therapy in the presence of point heating power are presented to investigate efficiency of the proposed technique.
LA - eng
KW - optimal control; Pennes' bioheat equation; semigroup theory; thermal therapy; hyperthermia; optimal control; Pennes' bioheat equation; semigroup theory; thermal therapy; hyperthermia
UR - http://eudml.org/doc/262004
ER -

References

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  11. Heidari, H., Zwart, H., Malek, A., Controllability and Stability of 3D Heat Conduction Equation in a Submicroscale Thin Film., Department of Applied Mathematics, University of Twente, Enschede 2010, pp. 1-21. 
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