Inverse problems of electromagnetic sounding: Gradient medium and periodic boundary

The problems of the periodic interface profile reconstruction and the recognition of dielectric constant of the layered medium according to the values of the reflection coefficients for a finite set of probing frequencies are rather urgent in connection with the development of modern non-destructive testing methods. To solve them the original problems are reduced to the search for the optimal control (the profile of the dielectric constant) of the Cauchy problem for the Riccati equation. Construction of optimal control in the class of polynomial functions is based on the minimization of the corresponding functional. The criterion of selection of polynomial approximations for profile permittivity uses the separation of input data into Training and Testing sequences of probing frequency. An analysis of errors of the reconstruction of the imaginary part of permittivity of the layered medium was carried out.