The urgency of the problem is caused by that the correct analysis and synthesis of non-stationary control systems should start with studying the properties of the exact solution of the Cauchy problem. However the absence of the exact analytical solution of the non-stationary systems of differential equations considered necessitates the use of approximate models.
The models obtained using various algorithms of approximate summation of asymptotical decompositions of the exact solution of the Cauchy problem are considered. For the first time the approximate models taking into account values of the exact solution at the initial and final points of the trajectory are constructed.