ABSTRACT
The article introduces a new concept of price-target invariance of dynamical system optimal controls. Several types of optimization problems have been discovered in which, in the process of analyzing the necessary conditions, it is possible to obtain relations between control functions that are independent of the initial and final conditions for maneuver and criterion for assessing the quality of control. These relationships appear to violate the Leibniz sufficient reason principle. The relevance of determining the nature of these relationships is due to the need to solve the problem of the possibility of their practical use, which greatly simplifies the structure of the facility’s control system.
Below are the results of the study of invariant relations of both regular and singular controls of the motion of dynamical systems. The latter turned out to be especially effective in controlling the movement of aircraft in the atmosphere as well as in controlling devices with propulsion systems that use engines with various methods of thrust generating. In the case of controlled objects, the motion of which is described by systems of linear equations with constant coefficients, there are the invariant relations indicated by the 168Feldbaum between the moments of control functions switching. An analysis of these relations showed that oscillatory systems possess, in addition to the known time constant, the energy time constant. This article establishes this constant dynamic meaning. The new principle is proposed as a form of the universal minimum energy dissipation principle, specific for describing processes in living nature.
