Applied Mathematics and Control Sciences

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.

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.

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).

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.

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.