Optimization method in two-dimensional electrical cloaking problems

In this paper, we study control problems for the two-dimensional electrical cloaking model in the case when the cloaking device has shape of a ring filled with an inhomogeneous anisotropic medium. These problems arise while developing technologies of design of electrical cloaking devices using an optimization method for solving inverse problems. The solvability of the direct and control problems for considered electrical transmission model is proved. The optimality system that describes the necessary conditions for an extremum is derived, and its properties are investigated. The possibility of implementing two types of numerical algorithms that are used to find approximate solutions is discussed.