This paper presents a generalization of iterative dynamic programming using Luus-Jakola optimization procedure applied to the solution of optimal feed-back control for nonlinear deterministic systems. Iterative dynamic programming is realized. Efficiency of proposed method is tested on the software complex developed by the authors in C++; a model example of chemical process control is presented.

The article deals with the optimal filtering and extrapolation problems for non-stationary stochastic differential systems with a Poisson component. To find an approximate density of the observed object’s state vector the spectral method based on the representation of robust Duncan-Mortensen-Zakai equation and Kolmogorov-Feller equation solutions in the form of orthogonal series is used.

A description of the Galilean symmetry invariant solutions to the KdV-Burgers equation is reduced to studying of phase trajectories of the corresponding ODE depending on a parameter (the velocity of a shock wave propagation). Exact invariant solutions are simple shock waves that become separatrixes on the phase portrait which always has two singular points for a given value of the parameter. For nonlinear superposition of shock waves the phase portrait contains four singular points; its consequent bifurcations lead to oscillations.

An approach to the problem of estimating an aerodrome airspace capacity based on the idea of airspace «quantization» and transition to discrete time while imposing restrictions on the filling of quantum states by aircrafts has been developed in this paper. It is shown that such a formalism can significantly reduce the complexity of aircrafts movement simulation in the airfield zone, to take into account the restrictions imposed on the aerodrome airspace capacity by intersections of arrival and departure routes. The paper presents the results of the simulation experiment, illustrating the dependence of the aerodrome airspace capacity upon the number of aircraft routes intersections, v.kuznetsov@mstuca.aero.

The paper contains algorithms for solving the problem of nonlinear filtering. The nonlinear approximate filters presented are: the extended Kalman filter (EKF), the uncented Kalman filter (UKF) and unscented Particle Filter (UPF). The flow-charts for the listed algorithms are presented and a corresponding software complex based on these algorithms is developed. Using this complex a number of worked-out numerical simulations for both linear and nonlinear models are resulted.

This paper presents a hybrid memetic algorithm for finding a conditional global extremum of functions. The algorithm combines such characteristics as modularity and adaptability which provides flexibility and controllability of the algorithm and reduces the influence of parameters. On the basis of the proposed algorithm the software complex is formed in the C# language. The method effectiveness is demonstrated on several well-known model examples of finding a conditional global extremum for functions of several variables.

The theoretical problems of computer support for the "System Wide Information Management" concept, which was proposed by experts of the International Civil Aviation Organization, are discussed. Within the framework of its provisions certain new requirements for all initial stages of air traffic management preceding the direct aircrafts control are formulated. Algorithmic instruments for ensuring a conflictlessness of a summary plan for the use of airspace during the plan’s implementation are analyzed.

Methods of theoretical group analysis of differential equations are applied to the k -ε turbulence model. Symmetry reductions of the k -ε turbulence model with respect to some three-dimensional symmetry subalgebras are considered. Families of exact solutions are obtained.

The article is devoted to the search of optimal control in a model of a middle-distance running in order to minimize the time spent. Control is the force exerted by a sportsman per unit mass - or rather, the acceleration. The initial conditions and constraints on the control are prescribed. In the article optimal control problem is reduced to a fixed-time one by introducing the coefficient of compression of time, which is the second controlling factor.

Properties of continuous positively homogeneous operators of degree via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space are studied. Necessary and sufficient conditions for these functions to vanish on the image of the unit ball under positively homogeneous operators are given. In particular, we give criteria for the complete continuity of the Fréchet derivative in an arbitrary Banach space and criteria for operators, acting in regular spaces, to be improving.

We find contact integrable extensions and coverings for the r-th double modified dispersionless Kadomtsev-Petviashvili law equation. One of the coverings provides a Bäcklund auto-transformation and a recursion operator for the equation under the study.

First let's construct the determined model of the dynamic of uncontrolled epidemiological process. The quotient β describes frequency of meetings of sick people with healthy and probability of infection. It is subject to action of random factors. Let's enter an item for it which will take into account the influence of a random destabilization. We'll have stochastic model of epidemic. Comparing the determined and stochastic models, we'll find admissible borders for destabilizing quotient σ if the maximum deviation of dynamic variables can not be higher than 5 %.

This paper analyzes the patterns of early repayment in multi-period credit transactions. Considered one of the most common ways of conversion of unpaid interest for early repayment, so-called 78 rule. The relationship of this rule with the linear approximation of the exact value; redeemable debt is determined. The analysis of the maximum excess payment of interest on 78 rule. It has been shown how interest payment on 78 rule depended on the time of early repayment.

Early repayment of debt is an agreement under which the borrower pays to the lender amount of money equal to the current balance (as of loan account). Then further regular payments cease and the contract terminates. However, the amount of outstanding debt is determined by the structure of prescription charges. So in the uniform schemes of repayment of consumer credit each payment contains the same part of principal amounts and the total interest. In case of early repayment the Bank loses a significant fraction of the expected interest payments. Therefore, in practice, often used so-called accelerated schemes of interest payments. One of them is 78 rule. Use the 78 rule is simple and straightforward. The name of the rule is due to the fact that the sum of the numbers 12 monthly payments is 78. In the schemes of consumer loan with a term of one year interest payment for the current month is equal to m/78 of the total amount of interest payments, where m is the number of remaining payments. The rule name is stored and in the more general case with an arbitrary number of payments. In general interest payment is determined by the relative weight of the total amount of interest in each payment. In uniform schemes it is constant. In accelerated with a particular speed decreases. Therefore, additional cash expenses by the 78 rule may be considered as additional penalties for early repayment of the debt. It this article is shown how this penalty depends on time before maturity. It is shown that the magnitude of these penalties in monetary terms reaches the maximum value when the loan is repaid early between half and two thirds of the total of the loan term.

A construction of building of diffeomorphisms which preserve the ball volume and are identity on boundary has proposed. A behavior of hydrodynamics incompressible fluid solutions with initial condition being null on the boundary is investigated.

The paper deals with a mathematical model of network security. The model is described in terms of the nonlinear optimal control. As a criterion of the control problem quality the price of the summary damage inflicted by the harmful codes is chosen, under additional restriction: the number of recovered nodes is maximized. The Pontryagin maximum principle for construction of the optimal decisions is formulated. The number of switching points of the optimal control is found. The explicit form of optimal control is given using the Lagrange multipliers method.

The factors that have impact on the choice for the passenger air fare tariffs are ordered in a modern way to reflect their importance. The new features of the paper are the objects of research - the fare rules conditions, which are a formalized data tariff of global distribution systems (GDS) or computerized reservation systems (CRS). The application of the developed method results in obtaining a number of objects that have a significant impact on the value of the fare selected.

The paper deals with the main methods for solving equations with redundancy. It is subsequently used for modelling the ground many-positional system as a part of a system for analysis of air navigation data as a whole. In particular, the least square method and the Taylor series method are modelled taking into account the impact of stochastic factors influencing the system output. The factors with maximal effect on the accuracy of the functioning of the ground many-positional system are determined; a comparative analysis of the methods is carried on.