Separation of Optimal Controlled Motion into Components

As a result of analytical and numerical experiments, an analytical control dependence (translational acceleration) on the polynomial degree is found and investigated; the total movement and motion time are set in advance. If the degree of acceleration polynomial increases, energy costs to realize the optimal object motion (acceleration-braking type) decrease. The smallest polynomial degree is 1 and the known classical control follows. If the degree (it is always odd) increases, then less energy-intensive control appears. In all cases, quiescence occurs in the final position and control is turned off. The designing algorithm leads to universal analytic dependencies and it is based on the reversive optimality principle, the ultimate purpose of which is a reconstructed functional-criterion that takes on a minimum value. The algorithmic features of the constructed control are noted, and its comparison with the known one (that was found using the variational method of the optimal control theory) is given. It is shown that it is possible to separate the phases of controlled motion into acceleration, uniform movement and deceleration. This object's sequential motions implementation is illustrated by numerical example when comparing classical and constructed controls. A special function "picewise" (from the Maple) is used to obtain a graphical description of the motion model. The conclusion draws attention to the applications of research results in various fields of modern technology.