## No 4 (2016)

SECOND ORDER NECESSARY OPTIMALITY CONDITIONS FOR CONTROLS PROBLEM OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY ARGUMENT

#### Abstract

The problem optimal controls of nonlinear stochastic systems such that behavior is given by Ito stochastic differential equations with delay argument. The optimality criterion is the expectation of terminal functional. With the first and second variation (the classical sense) of quality functional necessary optimality conditions first and second orders are obtained. In particular case from establishment second order necessary condition stochastic analog of Legendre-Clebsch and other series constructively testable results received. The end considered the degeneration case of the Legendre-Clebsch condition and different necessary optimality conditions for singular, the classical sense control obtained.

**Applied Mathematics and Control Sciences**. 2016;(4):7-26

On invertibility of A linear operator connected with singular differential equations

#### Abstract

In this paper a representations of inverse and right inverse operators for operator of the form I + kC a on the Lebesgue space L 2 were obtained. Here I - identity operator and C a generalized Cesaro operator, k - real parameter. Such operator appears while studying various singular differential equations. The results can be used to study boundary value problems for singular differential equations, including the study of the asymptotic behavior of solutions.

**Applied Mathematics and Control Sciences**. 2016;(4):27-35

MATHEMATICAL MODELING OF THE FORMAL ANALOGY OF ELECTROMAGNETIC FIELD

#### Abstract

It is shown that the classical model of the magnetic field violates Newton’s third law, excludes interaction elements coaxial conductors with currents, does not provide for the existence of the moments of the forces acting on the elements of the conductors, and the direction of the field vector does not coincide with the direction of the force acting on an element of the conductor with current induction depends on the properties of the medium, and the intensity - no, the divergence of the field is equal to zero, Ampere's law is considered to be a formula in the general case is incompatible with its main result, the law of electromagnetic induction is phenomenological. A model of a formal analogue of the electromagnetic field, which has no specified features, in particular, the formal analogy of the law of electromagnetic induction is a simple consequence of the other properties and relations of the field, while the constructed model satisfies the basic requirement Ampere - unconditional implementation of Newton's third law.

**Applied Mathematics and Control Sciences**. 2016;(4):36-60

ONE APPROACH TO SOLVING THE PROBLEM OF DISCRIMINANT ANALYSIS MICROSTRUCTURES FUNCTIONAL MATERIALS ON A COMPLEX OF PHYSICAL AND MECHANICAL PROPERTIES

#### Abstract

This article considered one of the approaches to solving the problem of discriminant analysis of microstructures functional materials on a complex of physical and mechanical characteristics, based on the theory of fuzzy sets. The proposed approach can be use in the process of selective quality control of the functional and structural materials. It is assumed that the initial data for tasks of discriminant analysis can be obtain from of computer pattern recognition in the analysis of the microstructure of the material on digital images of microsection. An algorithm for solving the problem of discriminant analysis of grain-phase structures, which allows determining the proximity of the material to one of the classes on a given set of known structures on the complex physical and mechanical characteristics. Authors present a demo of the application of the developed algorithm in the analysis of microstructures on photographs microsections hardened steel with desired strength properties.

**Applied Mathematics and Control Sciences**. 2016;(4):63-85

FUNCTIONAL COMPLETE TOLERANT LOGIC ELEMENTS FOR FAULT TOLERANT AUTOMATED SYSTEMS

#### Abstract

Functional and complete (in the sense of Theorem Post) tolerant elements have been proposed as a paradigm spread structurally stable computers, proposed by Professor V.A. Kharitonov, at the turn of the 90s of the twentieth century, on the register transfer level. Structurally stable computers have the ability to emulate the desired command system in case of failure of individual teams from the original set. In turn, functionally complete tolerant logic elements FCTLE have the ability of maintaining the functional completeness of a given model of failures. In 1996-1997 FСT were obtained function model considering the constant failure of one of the four inputs of the corresponding element (stuck-at-0; stuck-at-1). They were the composition of AND, OR, NOT logic functions. Of these, the practical significance of known functions 2OR-2AND-NOT; 2AND-2OR-NOT. When adding Bridging Faults: (Dominant; Wired AND, OR; Dominant AND / OR), it proved that the cardinality of the set of functions FPT reduced, but 2OR-2AND-NOT; 2AND-2OR-NOT maintain tolerance. Then there were the issues of maintaining the functional completeness at the transistor level for internal failures logic element (valve) KMOS transistors (stuck-closed transistor - permanently closed, stuck-open transistor permanently open. It is shown that the functional completeness is preserved in case of failure of one transistor or a top of the circuit - connect “+” power supply or lower - bus connection “Ground”. Then came the understanding that can be similar to conserve not only the functional completeness, but also the realization of a function at the level of a single element. The article features FCTLE elements included in the FPGA with the so-called LUT (look up table).

**Applied Mathematics and Control Sciences**. 2016;(4):89-105

A method of calibrating instruments for the measurement of residual stresses

#### Abstract

In the design and manufacture of products for critical applications one of the regulated parameter is the level of residual macrostresses. To control the level of residual macrostresses actual use of nondestructive testing, such as X-ray diffraction method and the method of the Barkhausen noise. When using these methods, an important step is the calibration of equipment - setting the zero level RS1 includes using reference samples. The shortcomings of the existing reference samples. A method for calibration using flat specimens deformed by bending scheme.

**Applied Mathematics and Control Sciences**. 2016;(4):106-114

NETWORK-CENTRIC ASPECTS OF MODERN PRODUCTION MANAGEMENT STRATEGIES

#### Abstract

The paper presents a review of modern approaches to the management of industrial enterprises. The widespread use of these approaches the principles of decentralized group control is shown. In accordance with these principles management functions are passed from upper layers to the departments of the enterprise. As a result, the departments of the enterprise can significantly increase the efficiency and effectiveness of solutions. In particular, the departments of the enterprise waive automation centralized production planning at the operational level.

**Applied Mathematics and Control Sciences**. 2016;(4):115-124

Optimal stabilizing control in the problem of optical fiber drawing

#### Abstract

We consider the optimal control problem for a distributed control system with a compromise. We show solvability and obtained an optimization system for optimal control problems with boundary control, described by the equations of continuity and motion melts.

**Applied Mathematics and Control Sciences**. 2016;(4):125-134

The matrix anonymous generalized median schemes with delegation

#### Abstract

Approaches to design vote procedures with delegation messages at the matrix anonymous generalized median scheme are discussed in this paper. One of approaches based on idea - if the expert considers it necessary to delegate the message about any criteria, then he should include result of active examination, which would have made without the participation of an expert. Another design of votes procedures with delegation based on filling the convolution matrix on the basis of total domination over the criterion on which the message is scheduled to delegate.

**Applied Mathematics and Control Sciences**. 2016;(4):137-156