Synthesis of Adequate Mathematical Description as Solution of Special Inverse Problems

Abstract. The problem of mathematical simulation of dynamic system characteristics behavior and their adequacy to real experimental data, which correspond to these characteristics, is considered in this paper. The specified problem is still poorly investigated and hardly adapted to formalization. The requirements of related to the adequate mathematical simulation of dynamic system are considered for the case when mathematical description is represented by system of the ordinary differential equations. The conditions are obtained which allow to reduce a problem of the adequate mathematical description to the solution of the several integral equations of the first type. The methods of obtaining of the steady solutions are suggested. The domains of application of the obtained solutions are specified. For a case, when the differential equations of dynamic system are given with errors in coefficients, several variants of synthesis of the adequate mathematical descriptions depending on final goals of this description use are suggested. The examples of the adequate descriptions of concrete dynamic systems are given