Applied Mathematics and Control Sciences

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.

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.

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.

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.