Abstract
A brief review of the works of the author and his co-authors on the application of nonlinear analysis, numerical and analytical methods for solving the nonlinear inverse problems (synthesis problems) for optimizing the different types of radiating systems, is presented in the paper. The synthesis problems are formulated in variational statements and further they are reduced to research and numerical solution of nonlinear integral equations of Hammerstein type. The existence theorems are proof, the investigation methods of nonuniqueness problem of solutions and numerical algorithms of finding the optimal solutions are proved.
Highlights
In many practical applications at the optimal design of various types of radio and acoustic radiating systems the requirements are only to the energy characteristics of the directivity of the radiated field (amplitude directivity pattern (DP) or DP by the power)
The synthesis problems are formulated in variational statements and further they are reduced to research and numerical solution of nonlinear integral equations of Hammerstein type
Later on we shall consider the synthesis problem of a flat aperture, in which in addition to amplitude-phase distribution (APD) desired is too the function that describes the boundary of aperture
Summary
In many practical applications at the optimal design of various types of radio and acoustic radiating systems the requirements are only to the energy characteristics of the directivity of the radiated field (amplitude directivity pattern (DP) or DP by the power). The degenerate of kernels in linear operators of the Hammerstein type equations is feature of the synthesis problems of antenna arrays It allows to reduce nonlinear two-parameter spectral problems on finding the set of branching points of solutions to the corresponding systems of linear algebraic equations with nonlinear occurrence of the spectral parameters in the coefficients of system. An important feature of the variational formulation of synthesis problems is the fact that in the optimization criterion can introduce functionals describing certain other requirements to amplitude-phase distribution (APD) of outside excitation sources. Their mean-square deviation, as a rule, will be used as the criterion of proximity of amplitudes of the given and synthesized DP
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