Geodesic
Optimal control solution for Pennes' equation using strongly continuous semigroup
Kybernetika, Tome 50 (2014) no. 4, pp. 530-543.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.14736/kyb-2014-4-0530
Classification : 62A10, 92C30, 93B40, 93C95, 93E12
Keywords: optimal control; Pennes' bioheat equation; semigroup theory; thermal therapy; hyperthermia 
@article{10_14736_kyb_2014_4_0530,
     author = {Malek, Alaeddin and Abbasi, Ghasem},
     title = {Optimal control solution for {Pennes'} equation using strongly continuous semigroup},
     journal = {Kybernetika},
     pages = {530--543},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2014},
     doi = {10.14736/kyb-2014-4-0530},
     mrnumber = {3275083},
     zbl = {06386425},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-4-0530/}
}
TY  - JOUR
AU  - Malek, Alaeddin
AU  - Abbasi, Ghasem
TI  - Optimal control solution for Pennes' equation using strongly continuous semigroup
JO  - Kybernetika
PY  - 2014
SP  - 530
EP  - 543
VL  - 50
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-4-0530/
DO  - 10.14736/kyb-2014-4-0530
LA  - en
ID  - 10_14736_kyb_2014_4_0530
ER  - 
%0 Journal Article
%A Malek, Alaeddin
%A Abbasi, Ghasem
%T Optimal control solution for Pennes' equation using strongly continuous semigroup
%J Kybernetika
%D 2014
%P 530-543
%V 50
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-4-0530/
%R 10.14736/kyb-2014-4-0530
%G en
%F 10_14736_kyb_2014_4_0530
Malek, Alaeddin; Abbasi, Ghasem. Optimal control solution for Pennes' equation using strongly continuous semigroup. Kybernetika, Tome 50 (2014) no. 4, pp. 530-543. doi : 10.14736/kyb-2014-4-0530. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-4-0530/

Cité par Sources :