ПРИНЦИП И ТЕОРЕМЫ РЕВЕРСИОННОГО ИСЧИСЛЕНИЯ

Abstract

A reverse optimality principle (ROP) is formulated and an algorithm for its use for constructing optimal portable object movements is presented. Using an example, sufficient conditions for the extremality of the restored criterion functional are verified when constructing an optimal control of the «acceleration–deceleration» type. The following theorems were formulated and proved: on the numerical equality of integrals with different integral functions, on the minimum energy to achieve the goal of optimally controlled motion in the form of «acceleration–deceleration». Basing on the generalization of the results for optimal controls designing of the «acceleration–deceleration» type of motion, whence the known special cases follow, universal analytical control function (translational acceleration) was found. Analytically and numerically was confirmed the existence of the limiting minimum control energy at which the movement of an object from the initial state of rest to a new state of rest is possible at a fixed distance and time of motion.