We consider the problem of mathematical modeling and computer simulation of nonlinear controlled dynamical systems represented by differential-algebraic equations of index 1. The problem is proposed to be solved in the framework of a neural network based semi-empirical approach combining theoretical knowledge for the object with training tools of artificial neural network field. Special form neural network based semi-empirical models implementing an implicit scheme of numerical integration inside the activation function are proposed. The training of the semi-empirical model allows elaborating the models of aerodynamic coefficients implemented as a part of it. A semi-empirical model using as theoretical knowledge the equations of the full model of the hypersonic vehicle motion in the specific phase of descent in the atmosphere are presented. The results of simulation for the identification task for the aerodynamic pitching moment coefficient implemented as an ANN-module of the semi-empirical model of the hypersonic vehicle motion are presented.
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