The work begins with an essay on ancient Greek philosophy: since it was this philosophy that largely shaped the course of thought in the subsequent centuries, the general direction, and con-tent in the scientific context, and laid down ideas, including the concept of symmetry, which underlies the physics of today of the day when humanity makes a breakthrough for the transition to an innovative society. It is shown how the concepts introduced by the Greeks evolved in modern times in interaction with new knowledge, acquiring over time an increasingly rigorous and complete mathematical description, what an important role it played in physics. Nowadays, symmetry is defined as a set of properties: order, uniformity, proportionality, harmony. All signs of symmetry in many of its definitions are considered equal, equally significant, and in certain specific cases, when establishing the symmetry of a phenomenon, any of them can be used. In some cases, symmetry is homogeneity, in others it is dimensionality. Further, the modeling of navigation high-speed complex technical systems by the method of symmetry theory is considered. The issues of identification in the local area and restoration of the phase portrait of navigation high-speed complex technical systems are considered. It is indicated that there is a symmetry of the shift of the system dynamics and the equal dimension of the parameters vector, which is caused by the group operation of shift in time, has the form of a linear function of time.