Method of additional argument in problems of optimal control

Ramiz RAFATOV

The problem of control of the process described by the nonlinear differential equation with partial derivatives of the first order, with conditions at t 0 and in a sequence n of points x1 < x2 ... < xn is solved. The criterion of quality of control is the integrated quadratic functional, which depends on a final state of system and set n of controlling parameters. The method of increment of functional is applied to reception of conditions of optimality, and the method of additional argument (MAA) is applied for the decision of the nonlinear equations with partial derivatives.

The Optimal Vector Control for the Elastic Oscillations Described by Fredholm Integral-Differential Equations

Elmira ABDILDAYEVA

In this paper, we investigate the nonlinear problem of the optimal vector control for oscillation processes described by Fredholm integro-differential equations in partial derivatives when function of external sources nonlinearly depend on control parameters. It was found that the system of nonlinear integral equations,which obtained relatively to the components of the optimal vector control, have the property of equal relations. This fact lets us to simplify the procedure of the constructing the solution of the nonlinear optimization problem. We have developed algorithm for constructing the s ...More

Using the Cramer-Gauss Method to Solve Systems of Linear Algebraic Equations with Tridiagonal and Five-Diagonal Coefficient Matrices

Anarkül URDALETOVA

It is known that among the methods used in solving systems of linear algebraic equations, the Cramer method has a number of disadvantages compared to the Gauss method, in particular: the inability to write out solutions to a system that has many solutions; the cumbersomeness of calculations with large system size. However, when applied to systems with a square matrix, it is, in a sense, more convenient than the Gauss method. The authors of this work developed and proposed a method in which they tried to combine the advantages of the Cramer and Gauss methods. In this paper, the Cramer-Gauss met ...More

On the R -compactification of uniform spaces

As it is well known, there are various constructions of the R-compactification (Hewitt real compactification) of a uniform space [13], [15]. In this work we propose a new construction of the R-compactification (Hewitt real compactification) of a uniform space. Keyword: A0-boundedness; R-compactification; R-completeness.; R-extension

On the Solvability of a Boundary Value Problem for Nonlinear Optimization of Oscillatory Processes

Elmira ABDILDAYEVA

The paper investigates the solvability of a boundary value problem in the control of an oscillatory process described by control in partial derivatives of the first order. It has been established that there are an infinite set of controls, as solutions to the system of nonlinear Fredholm integral equations of the first kind, each of which transfers the controlled process from the initial state to the final specified state in a specified time. Sufficient conditions for the existence of a nonlinear optimization solution are found.

Asymptotics of the Solution of Parabolic Problems with Multipoint Stationary Phase

Asan ÖMÜRALİEV | Ella ABILAYEVA

The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem when the limit operator has not range and with rapidly oscillating free term, its derivative of the phase vanishes at finite points. The vanishing of the first derivative of the phase of the free term induces transition layers. It is shown that the asymptotic solution of the problem contains parabolic, inner, corner and rapidly oscillating boundary-layer functions. Corner boundary-layer functions have two components: the first component is described by the product of parabo ...More

On Solvability of Optimization Problem for Elastic Oscillations with Multipoint Sources of Control

Elmira ABDILDAYEVA

In the paper we investigate the optimal control problem for elastic oscillation under multipoint influences of external forces when oscillation process is described by Fredholm integro-differential equation. Sufficient conditions for unique solvability of nonlinear optimization problem were found and the algorithm for constructing complete solution to this problem was developed.

On the Solvability of a Nonlinear Tracking Problem Under Boundary Control for the Elastic Oscillations Described by Fredholm Integro-Differential Equations

Elmira ABDILDAYEVA

In the present paper we investigate nonlinear tracking problem under boundary control for the oscillation processes described by Fredholm integro-differential equations. When we investigate this problem we use notion of a weak generalized solution of the boundary value problem. Based on the maximum principle for distributed systems we obtain optimality conditions from which follow the nonlinear integral equation of optimal control and the differential inequality.We have developed an algorithm to construct the optimization problem solution. This solving method of a nonlinear tracking problem is ...More

Solutions of the Rational Difference Equations xn+1 = xn-11/1+xn-2xn-5xn-8

Dağıstan ŞİMŞEK | Burak OĞUL

In this paper a solution of the following difference equation xn+1=xn-111+xn-2xn-5xn-8 was investigated, where x-11, x-10, ..., x-2, x-1, x0 ∈ (0, ∞).

Topology of Soft Cone Metric Spaces

Dağıstan ŞİMŞEK

In Simsek's paper it was introduced a concept of soft cone metric space via soft elements and some fixed point theorems in soft cone metric space were provided. In this work, we examine topological structures such as open ball, soft neighbourhood and soft open set in soft metric spaces and their some properties, and prove that every soft cone metric space under some condition is a soft topological space according to elementary operations on soft sets.

Formulas for solution of Riccati's equationle

Avıt ASANOV

In this paper we obtained the formula for the common solution of Riccati equations. Here Riccati equations was solved for common cases. Results obtained have been compared with the conventional ones and a comment has been made on them.

Uniformities for Wallman compactifications and realcompactifications

Asılbek ÇEKEEV

The natural methods of uniform topology for construction of Wallman compactifications and Wallman realcompactifications are developed. Results on partial order and relations of dimensions in the lattice of compactifications are presented. The construction of the maximal compactification among compactifications of X with fixed realcompactification is given. - MSC 54E15; 54D35; 54D60; 54F45 . - Keywords: Uniformity; (Wallman, β-like) compactification; (Wallman) realcompactification; Normal base; Dimension