## No 4 (2017)

LINEARIZED AND GUADRATIC NECESSARY OPTIMALITY CONDITIONS IN ONE BOUNDARY CONTROL PROBLEMS FO GOURSAT-DARBOUX SYSTEMS

#### Abstract

In the paper investigated boundary optimal control problem for Goursat-Darboux systems assuming the convex of control domain. Analogous linearization maximum condition is obtained. Necessary optimality conditions of quasi-singular controls are derived.

**Applied Mathematics and Control Sciences**. 2017;(4):7-28

AN EXAMPLE OF THE IDENTIFICATION ALGORITHM OF THE DYNAMIC CONTROL OBJECT WITH A PRIORI CONSTRAINTS

#### Abstract

An algorithm of identification of dynamic object with a priori limitation of the control object. The article contains an example of the algorithm of identification of dynamic object with a priori restrictions. The algorithm requires a large amount of computational resources due to the number of all possible combinations of rows. Examines the work of the ad hoc algorithm to identify the dynamic object of control, allowing to transform the original data in block unit is converted from the original data. After unit conversion of the source data there is a possibility of random selection of n rows from the source data unit is converted. This reduces the problem of search identification of a dynamic object to the identification of a static object.

**Applied Mathematics and Control Sciences**. 2017;(4):29-42

ON THE SOLVABILITY OF THE BOUNDARY-VALUE PROBLEM FOR A QUASILINEAR NEUTRAL TYPE EQUATION

#### Abstract

The boundary problem for a quasi-linear differential neutral-type equation is considered. The boundary condition of the problem is given by a general linear bounded functional defined on the space of absolutely continuous functions. For the problem in question, the sufficient conditions of the existence of at least one solution are obtained.

**Applied Mathematics and Control Sciences**. 2017;(4):43-50

MODEL OF VISCOELASTIC THERMOMECHANICAL BEHAVIOR OF FIBROUS COMPOSITE AND ITS EXPERIMENTAL IDENTIFICATION

#### Abstract

Phenomenological determining relationships for fibrous composite materials under the conditions of thermo-relaxation (vitrification) transitions are created. The model is based on the approach used earlier by the authors to describe the thermomechanical behavior of glassy amorphous polymers with a generalization to the class of anisotropic glass materials. A technique for the experimental identification of the obtained physical model was developed and implemented. On the example of two materials - epoxy binder and fabric glass fiber reinforced plastic on its basis thermomechanical constants included in the model were obtained. In the testing experiments, the adequacy of the proposed approach was confirmed.

**Applied Mathematics and Control Sciences**. 2017;(4):51-72

StABILITY OF inverted PENDULUM with delayed feedback

#### Abstract

A model of an inverted pendulum with delayed feedback is considered. The model is a second order linear autonomous differential equation with two delays. The ratio of delays is one to two. The criterion for the asymptotic stability of the equation is obtained by the method of D-subdivision.

**Applied Mathematics and Control Sciences**. 2017;(4):73-87

EFFECTIVE STABILITY CRITERION FOR A DISCRETE DYNAMICAL SYSTEM

#### Abstract

We consider the problem of the exponential stability of an autonomous difference equation. As is known, the problem is reduced to the Schur-Cohn problem of obtaining the number of roots of a polynomial which are inside the unit circle of the complex plane. In contrast to known approaches based on the methods of complex analysis and linear algebra, or on the reduction to the Routh-Hurwitz problem for the number of roots of a polynomial in the left half-plane, we propose the proof of the Schur-Cohn theorem by using the D-decomposition method. The presented approach is simple and explicitly relates the classical methods traditionally considered as independent.

**Applied Mathematics and Control Sciences**. 2017;(4):88-103

SYSTEMATIC APPROACH TO THE OPTIMIZATION OF NON-AUTOCLAVED AERATED CONCRETE PRODUCTION TECHNOLOGICAL PROCESS

#### Abstract

A new optimization method of non-autoclaved aerated concrete production process in terms of unstable quality raw materials use is presented in this article. The proposed method is based on a two well-known methods synthesis: method of expert systems and the Nelder-Mead method. The presented approach allows to achieving a synergistic effect, which is a significant decrease in the average number of experiments needed to adapt the material production process to unstable properties raw materials use.

**Applied Mathematics and Control Sciences**. 2017;(4):107-117

INFLUENCE OF TECHNOLOGICAL PARAMETERS OF PRODUCTION ON THE LEVEL OF RESIDUAL STRESES IN COVERS OF FUEL ELEMENTS

#### Abstract

In work the analysis of influence of mechanical properties and technological parameters at a size and distribution of residual stresses is carried out by production of thin-walled covers of the heatallocating elements from zirconium alloys which are applied in the nuclear industry. Thus process of cold deformation by rolling of hollow axisymmetric products and a question of formation of residual stresses taking into account anisotropy of zirconium alloys is considered. In the analysis of residual tension the technique of determination of technological residual stresses on the basis of power approach is applied.

**Applied Mathematics and Control Sciences**. 2017;(4):118-133