Vol 22, No 3 (2017)

Properties of regular extremals in optimal control problems with equality and inequality state constraints are studied. It is proved that, under the regularity conditions, the strengthened Legendre condition implies Lipschitz continuity of the measure Lagrange multiplier from the maximum principle.

The Cauchy problem for a nonlinear functional-differential equation of general type with Volterra mappings is considered. Conditions of existence of a unique global solution and conditions of existence of a unique limitary prolonged solution are derived. The reduction to an operator equation with the Volterra operator in the space of continuous functions is used.

This is a third paper in the series devoted to singularities of geodesic flows in generalized Finsler (pseudo-Finsler) spaces. In two previous papers, we defined geodesics as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of the action functional, and studied generic singularities of so-defined geodesic flows in the case the pseudo-Finsler metric is given by a generic form of degree 3 on a two-dimensional manifold. In the present paper, we consider an important non-generic case: singularities of geodesic flows on two-dimensional surfaces embedded into the Berwald-Moor space of arbitrary dimension.

The paper discusses the problem of parametric identification of a structurally identified static polynomial system near the nominal mode in the case when only allowable limits are specified for states, controls and coefficients of the model.

Assertion about existence and evaluation of solutions to equations Yx, x =y , where the mapping Y acting in partially ordered spaces is covering by the first argument and antitone by the second argument is derived. This result is used for the proof of the Chaplygin’s type theorem on differential inequality with deviating argument.

The boundary value problems for a functional-differential inclusion generated by a multivalued map not necessarily convex-valued with respect to switching in the space of summable functions and with multi-valued impulses are considered. Concept of a generalized solution of such a problem is introduced. Existence conditions for a generalized solution of the boundary value problem are found. The effective estimates of generalized solutions are derived.

The article presents the definition of industrial and domestic sewage, their principal and staff are listed. The main task of the wastewater treatment facilities are described, the sewage treatment plant, its components are given. The purpose of the writing of this work lies in the prediction of the composition of mixed waste water, which is coming from households and industrial enterprises in a centralized system of water removal, after cleaning on the basis of dynamic linear and quadratic neighborhood models. The work is relevant because before draining waste waters into the pond, you must ensure that the information contained in their composition of impurities and contaminants do not exceed acceptable norms. In the article is presented the wastewater treatment process in the form neighborhood dynamic model, consisting of five nodes. The dynamic linear and quadratic neighborhood models are reviewed. The equations of recalculation of conditions and outputs for the intermediate and output nodes neighborhood models are given. The identification of dynamic linear and quadratic neighborhood models of wastewater treatment are performed, calculated average absolute errors for identification. The comparison of the results of dynamic linear and quadratic neighborhood models and the conclusion are produced.

Results about orderly covering multi-valued mappings are applied to studying functional inclusions in spaces of measurable functions. Existence conditions and estimates of solutions for such inclusions are obtained.