The automation of control processes by technical objects and technological processes in the different fields of industry, energetics and transport is accompanied by the broad use of tracking regulation systems intending for the reproduction at the output with the definite precision of the giving action, arbitrarily varying from the law which is unknown in advance. The methodology of the analytical synthesis of the optimal regulators (ASOR) called also as linear-quadratic (LQ) optimization has got the wide propagation in the automatic control theory. In the classical variant of setting up the ASOR problems are connected with stabilization of unperturbed motion of the object. The given settings don't take into account the wide class of the problems connected with the completeness (tracking) of the dynamic processes in environmental influences: here the channel of reference input defining the goal meaning of the directed output of the object is the integral structural factor of the automatic system. There are well known the tries to extend the ASOR methodology to control processes with the goal behavior of the object given by external (outer) standard models which are included themselves in control process and carry out the function of the generator of the standard output of the object. But the analysis of papers of the given direction shows its inapplicability for the wide class of control problems where the given action may be the arbitrary time function. In the given paper the methodology of use of LQ optimization for synthesis of servosystems, the function of which consists in tracking for variations a priori of unknown command order signal is discussed.