Mathematical model of joint optimization of programmed and perturbed motions in discrete systems

А new mathematical model for the optimization of discrete systems is constructed in the article. The program motion and the ensemble (beam) of perturbed motions are investigated. In this case, the authors consider the joint optimization of smooth and non-smooth functionals defined on the program and perturbed motions. The variation of the functional and the necessary optimality conditions are provided. The developed mathematical technique allows solving non-standard control and optimization problems in various fields of science and technology.

Justification of the program motion model for space-based Earth observation systems

статье рассматривается вопрос об автономном управлении космическими аппаратами (КА) в составе космических систем дистанционного зондирования Земли. Описана аналитическая модель программного движения КА, близкая к реальному движению, которая позволяет разработать и реализовать технологию автономного решения задач управления положением КА в заданной окрестности программного движения. Описаны свойства класса динамически устойчивых орбит. The article deals with the issue of autonomous control of spaceсraft (SC) as part of space Earth observation systems. An analytical model of the SC program motion close to the real motion is described, which allows developing and implementing a technology for autonomous control of the SC position in a given neighborhood of the program motion. Properties of a class of dynamically stable orbits are described.

PROGRAM MOTION OF UNLOADING MANIPULATORS

In the paper, the program motion of an unloading manipulator which is treated as a first integral of the considered system, is investigated. Currently, the popular way to solve such problem is the method of Lagrange multipliers. In the paper, the authors use another approach, the Priciple of Compatibility, in which the required program is treated as one of motion equations of the system. In the particular case, the program is considered as one of first integrals of the system. For illustrating the proposed method, the motion of an unloading manipulator of three degrees of freedom is considered.