ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

# оптимальное управление

## Approximation of the orientation equations of the orbital coordinate system by the weighted residuals method

In the quaternion formulation, the problem of mathematical modeling of the spacecraft movement in an elliptical orbit was considered. Control is an acceleration vector from jet thrust. Control modulus is constant. The control is directed orthogonally to the plane of the spacecraft orbit. The quaternion differential equation of an orbital coordinate system orientation was used to describe spacecraft movement.

## The problem of optimal control for singularly perturbed system with delay with integral quadratic con-straints

The control problem for the singularly perturbed system with delay with indeterminate initial conditions and integral quadratic constraints on the control resources according to the minimax criterion is considered. Procedure is proposed for construction initial approximation of control response for minimax problem of control.

## Determination of the Boundary in the Local Charzynski–Tammi Conjecture for the Fifth Coefficient

In this article we find the exact value ofM5 such that the symmetrized Pick function PM4(z) is an extreme in the local Charzynski– Tammi conjecture for the fifth Taylor coefficient of the normalized holomorphic bounded univalent functions

## About a problem of spacecraft's orbit optimal reorientation

The problem of optimal reorientation of the spacecraft's orbit is solved with the help of the Pontryagin maximum principle and quaternion equations. Control (thrust vector, orthogonal to the orbital plane) is limited in magnitude. Functional, which determines a quality of control process is weighted sum of time and module (or square) of control. We have formulated a differential boundary problems of reorientation of spacecraft's orbit.

## Using Galerkin Method for Solving Linear Optimal Control Problems

The linear optimal control problem is considered. Duration of the controlled process is fixed. It is necessary to minimize the functional, that characterizes the energy consumption. A method of constructing an approximate solution based on the Galerkin method is proposed. Examples of numerical solutions of the problem are given.

## Solution of a Problem of Spacecraft’s Orbit Optimal Reorientation Using Quaternion Equations of Orbital System of Coordinates Orientation

The problemof optimal reorientation of the spacecraft’s orbit is solved with the help of the Pontryagin maximum principle and quaternion equations. Control (thrust vector, orthogonal to the orbital plane) is limited inmagnitude. Functional, which determines a quality of control process, is weighted sum of time and impulse (or square) of control. We have formulated a differential boundary problems of reorientation of spacecraft’s orbit.

## Analytical Solution of Equations of Near-circular Spacecraft’s Orbit Orientation

The problem of optimal reorientation of spacecraft’s orbit with a limited control, orthogonal to the plane of spacecraft’s orbit, is considered. An approximate analytical solution of differential equations of near-circular spacecraft’s orbit orientation by control, that is permanent on adjacent parts of the active spacecraft’s motion, is obtained.

## Метод глобального улучшения для Гамильтоновых систем с управляемыми коэффициентами

Представлена новая модификация метода глобального улучшения управления на базе известного метода В. Ф. Кротова для задач управления гамильтоновыми системами одного класса. Проведены расчеты по управлению квантовой динамической системой, представляющей известную модель вращения плоской молекулы.

## Approximation of Control for Singularly Perturbed System with Delay with Geometric Constraints

The control problem for the singularly perturbed system with delay with indeterminate initial conditions and geometric constraints on the control resources according to the minimax criterion is considered. A limiting problem is formulated for which a specially selected quality functional is chosen. We propose the procedure for initial approximation construction of a control response in the control minimax problem.

## Solving Kinematic Problem of Optimal Nonlinear Stabilization of Arbitrary Program Movement of Free Rigid Body

The kinematic problem of nonlinear stabilization of arbitrary program motion of free rigid body is studied. Biquaternion kinematic equation of perturbed motion of a free rigid body is considered as a mathematical model of motion. Instant speed screw of body motion is considered as a control. There are two functionals that are to be minimized. Both of them characterize the integral quantity of energy costs of control and squared deviations of motion parameters of a free rigid body from their program values.