Vol 23, No 122 (2018)
Articles
113-124
125-130
131-135
ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR INCLUSIONS WITH CAUSAL MULTIOPERATORS AND THE METHOD OF INTEGRAL GUIDING POTENTIALS
Abstract
In the present paper the method of integral guiding potentials is applied to study the problem of the asymptotic behavior of solutions for a differential inclusion with a causal multioperator. At first we consider the case when the multioperator is closed and convex-valued. Then the case of a non-convex-valued and lower semicontinuous right-hand part is considered.
Russian Universities Reports. Mathematics. 2018;23(122):136-144
136-144
MODELING OF MULTISTRUCTURAL SYSTEMS ON MANIFOLDS FOR STATISTICAL ANALYSIS AND FILTERING PROBLEMS
Abstract
We propose an extension for the stochastic dynamical systems whose trajectories belong to a given manifold. This extension is the stochastic multistructural systems, namely the systems with a variable and random structure. The description for such systems are considered in application to analysis and filtering problems.
Russian Universities Reports. Mathematics. 2018;23(122):145-153
145-153
ON THE SPECTRAL PROBLEM AND POSITIVE SOLUTIONS FOR A FUNCTIONAL-DIFFERENTIAL EQUATION OF THE EVEN ORDER
Abstract
Basic properties of the system of eigenfunctions for even order functional differential equation under special boundary conditions are obtained. Equivalence of a serie of classical affirmations is established. Among them are the Vallee-Poussin affirmation and positivity of the corresponding quadratic functional.
Russian Universities Reports. Mathematics. 2018;23(122):154-157
154-157
DEGENERATED LINEARLY-QUADRATIC PROBLEM WITH DELAY
Abstract
We consider a degenerate linear-quadratic problem optimization with a constant delay in the system and in the functional. In the previously obtained results of the authors, it was possible to reduce the number of equations describing the parameters of optimal control. Thanks to this, for the first time model examples are calculated for such problems.
Russian Universities Reports. Mathematics. 2018;23(122):158-167
158-167
THE TEST VOLTERRA EQUATION OF THE FIRST KIND IN INTEGRAL MODELS OF DEVELOPING SYSTEMS CONTAINING n AGE GROUPS
Abstract
The paper addresses the test integral Volterra equations of the first kind in integral models of developing systems. Earlier, models consisted of two and three age groups of elements. Here the authors generalized the results to the case of an arbitrary number of groups. Along with the theoretical results, numerical calculations are given for the test example. Calculations illustrate the validity of theoretical estimates.
Russian Universities Reports. Mathematics. 2018;23(122):168-179
168-179
180-186
ON ASYMPTOTIC BEHAVIOR OF THE FUNDAMENTAL SOLUTION AND THE CAUCHY FUNCTION FOR NEUTRAL DIFFERENTIAL EQUATIONS
Abstract
We consider a linear autonomous neutral functional differential equation. We obtain formulas relating the fundamental solution and the Cauchy function for this equation. On the basis of the formulas the asymptotic behavior of solutions of the equation is studied.
Russian Universities Reports. Mathematics. 2018;23(122):187-199
187-199
THE PROBLEM OF OPTIMAL CONTROL FOR ONE SYSTEM OF LINEAR LOADED DIFFERENTIAL EQUATIONS
Abstract
The problems of control and of optimal control of a system of linear loaded differential equations are considered. The condition for the existence of program control and motion is formulated. An explicit form of the control action for the control problem is given and a constructive approach to solve the optimal control problem is proposed. As an application, a solution to the problem of optimal control of a concrete loaded system is constructed.
Russian Universities Reports. Mathematics. 2018;23(122):200-209
200-209
ABOUT COVERING MAPPINGS WITH VALUES IN THE SPACE WITH A REFLEXIVE BINARY RELATION
Abstract
The concept of orderly covers extend to mappings acting from an ordered space X into space Y with a reflexive binary relation. An assertion is obtained about the existence of a solution x∈X of the equation Υx, x = y, where y∈Y ; the mapping Υ :X 2 → Y one by one from the arguments is a covering, and on the other - antitone. An example of a concrete an equation satisfying the assumptions of the proved assertion, to which are not applicable known results, since Y is not an ordered space.
Russian Universities Reports. Mathematics. 2018;23(122):210-215
210-215
ON DIGITAL APPROXIMATIONS FOR PSEUDO-DIFFERENTIAL EQUATIONS AND RELATED BOUNDARY VALUE PROBLEMS
Abstract
We consider a discrete version of pseudo-differential operators as a first stage for constructing approximate methods of solving pseudo-differential equations and their numerical realization. For this purpose we introduce the classes of periodic symbols and discrete operators, study a solvability of corresponding discrete equations and suggest some computations algorithms.
Russian Universities Reports. Mathematics. 2018;23(122):216-227
216-227
228-234
ON THE WAVE EQUATION WITH THE HYSTERESIS TYPE CONDITION
Abstract
In this paper we investigate the initial-boundary value problem describing the oscillation process with a hysteresis-type boundary condition. This kind of problem arises in modeling of the string oscillations, where the movement is restricted by a sleeve concentrated at one point x = l: We suppose that the string is located along the segment [0 ; l ] and the sleeve can move in perpendicular to [0 ; l ] direction. The analog of d’Alembert formula is obtained. A boundary control problem is analyzed for a small period of time. The boundary control problem is to find a control function allowing to put the oscillation process from the initial state to the given final state.
Russian Universities Reports. Mathematics. 2018;23(122):235-242
235-242
THE INEQUALITY OF KARISTI AND GENERALIZED COMPRESSION (THE CASE OF SINGULAR IMAGES)
Abstract
In the present paper we consider a new inequality of Carity type and prove a theorem on a fixed point. Further, relying on the theorem obtained, we study maps (generalized contractions) that compress relative to some function of two vector arguments. This function does not need to be a metric or even continuous.
Russian Universities Reports. Mathematics. 2018;23(122):243-249
243-249
ALGORITHMS FOR SOLVING DIFFERENTIAL EQUATIONS IN MATH PARTNER
Abstract
Algorithms for finding the symbolic-numerical solution of linear inhomogeneous ordinary differential equations, Bernoulli equations are discussed. Algorithms for finding a solution through the Lagutinsky determinant are described. The description of Mathpar user language is given in the part that allows to use the service for solving differential equations.
Russian Universities Reports. Mathematics. 2018;23(122):250-260
250-260
ABOUT AN ESTIMATE FROM ABOVE OF THE FRACTIONAL DERIVATIVE OF THE COMPOSITION OF TWO FUNCTIONS
Abstract
In the paper, an estimate from above of the fractional Riemann-Liouville derivative of an order α∈0;1 of the composition of two functions is proved for the case when the inner function is assumed only to be represented by the fractional Riemann-Liouville integral of a measurable essentially bounded function. The necessity of such an estimate arises in control problems of dynamical systems described by differential equations with fractional derivatives.
Russian Universities Reports. Mathematics. 2018;23(122):261-267
261-267
HAMILTON-JACOBI EQUATIONS IN DYNAMICAL OPTIMIZATION PROBLEMS FOR NEUTRAL-TYPE SYSTEMS
Abstract
The relation between a differential game for neutral-type systems and a Hamilton-Jacobi functional equation with coinvariant derivatives is established. It is proved that the value functional of the game coincides with the minimax solution of this equation. Optimal strategies for the players are described.
Russian Universities Reports. Mathematics. 2018;23(122):268-277
268-277
ABOUT SINGULAR CONTROLS OF POINTWISE MAXIMUM PRINCIPLE FOR OPTIMIZATION PROBLEM CONNECTED WITH GOURSAT-DARBOUX SYSTEM
Abstract
In this paper, we consider the problem of maximizing a sufficiently general functional defined on solutions of the controlled nonlinear Goursat-Darboux system. The right-hand side of the differential equation is a Caratheodory function. We study singular controls in the sense of the pointwise maximum principle, i.e. the controls for which this principle degenerates. We consider strong degeneration of the pointwise maximum principle (this principle is the necessary first-order optimality conditions by using of needle-shaped variation of a control) when the maximum principle degenerates together with second-order optimality conditions. Sufficient conditions for the strong degeneration of maximum principle and necessary conditions for the optimality of corresponding singular controls are given. These conditions generalize the conditions that are known for the case of the terminal quality functional and the case of the smoother right side of the equation.
Russian Universities Reports. Mathematics. 2018;23(122):278-284
278-284
TO THE ITERATIVE METHOD OF CONSTRUCTING OPTIMAL CONTROL OF A SINGULARLY PERTURBED SYSTEM WITH DELAY WITH GEOMETRIC CONSTRAINTS
Abstract
The control problem for the singularly perturbed system with delay with indeterminate initial conditions and geometric constraints on the control resources according to the minimax criterion is considered. Procedure of constructing control response that approximates the optimal solution with given accuracy with respect to a small positive parameter is proposed.
Russian Universities Reports. Mathematics. 2018;23(122):285-291
285-291
292-302
THE STUDY OF A SINGUlARlY PERTURBED CONTROL SYSTEM
Abstract
The behavior of the control-functions and the state-functions (as the parameter tends to zero) for a linear stationary dynamical system with a small parameter at the system’s state functions derivative is studied. Complete conditions are formulated for the uniform aspiration of the control functions and the state of the initial system to the control functions and the state of the limiting system are formulated. A conditions at which the boundary layer phenomena near the edge points of the time interval appears are also formulated.
Russian Universities Reports. Mathematics. 2018;23(122):303-308
303-308
ON THE ALGORITHM FOR CONSTRUCTING REACHABLE SETS OF CONTROL SYSTEMS WITH ISOPERIMETRIC CONSTRAINTS
Abstract
We propose a method for constructing attainability sets for controllable systems with integral constraints on the control and trajectory of the system, which is based on the use of the Pontryagin maximum principle for characterizing the boundary points of the attainable set.
Russian Universities Reports. Mathematics. 2018;23(122):309-316
309-316
ON THE INITIAL-BOUNDARY VALUE PROBLEM FOR SEMILINEAR PARABOLIC EQUATION WITH CONTROLLED PRINCIPAL PART
Abstract
The first initial-boundary value problem for a semilinear parabolic equation with controlled coefficients of the main part is considered. Sufficient stability conditions (at perturbation of the controlled coefficients) of the existence of global solutions of the initial-boundary value problem are formulated.
Russian Universities Reports. Mathematics. 2018;23(122):317-324
317-324