Kybernetika 50 no. 4, 530-543, 2014

Optimal control solution for Pennes' equation using strongly continuous semigroup

Alaeddin Malek and Ghasem AbbasiDOI: 10.14736/kyb-2014-4-0530


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.


optimal control, Pennes' bioheat equation, semigroup theory, thermal therapy, hyperthermia


93E12, 62A10


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