Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
47
9
2015
On Solution of the Linear Matrix Equations
1-9
10.1615/JAutomatInfScien.v47.i9.10
Vladimir B.
Larin
S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
linear matrix equations
linear matrix inequalities algorithm
features of the desired solution
iterative procedures
accuracy
The algorithm of finding solutions of various types of the linear matrix equations is proposed. The algorithm is based on the linear matrix inequalities. It is noted that while using this algorithm, one is to take into account the features of the desired solution (a symmetric matrix, etc.). The possibility of using iterative procedures to improve the accuracy of solutions is considered. On the examples of solving various types of the linear matrix equations, the efficiency of proposed algorithm is shown.
Acoustic-Gravity Waves in Whirling Polar Thermosphere
10-22
10.1615/JAutomatInfScien.v47.i9.20
Yuriy P.
Ladikov-Royev
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
Oleg K.
Cheremnykh
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
Alla K.
Fedorenko
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev
Vladimir E.
Nabivach
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev
whirling polar thermosphere
acoustic-gravity waves
vortex motion of the medium
propagation towards the wind
mathematical model
The propagation of acoustic-gravity waves (AGW) in a rotating medium was investigated. In a simple model it has been shown that the AGW frequencies, close to the Bruntâˆ’Vaisala frequency, may occur in the presence of vortex motion of the medium. These waves propagate against the direction of rotation of the medium and have a horizontal scale of hundreds of kilometers. The obtained results enable one to explain the AGW main observed features in the polar thermosphere by the presence of background large-scale vortex motions.
Analysis of Queuing System with Dynamic Priorities
23-33
10.1615/JAutomatInfScien.v47.i9.30
Agasi Zarbali ogly
Melikov
Institute of Control Systems of National
Academy of Sciences of Azerbaijan, Baku
Leonid A.
Ponomarenko
International Research and Training Center of Information Technologies and Systems of National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kiev, Ukraine
Balami Gasym ogly
Ismailov
National Aviation Academy of Azerbaijan, Baku (Azerbaijan)
queuing system
dynamic priorities
multiplicative priority function
queues total length minimizing
simulation models
The queuing system with dynamic priorities which have a multiplicative form of the priority functions is considered. Solving the problem of minimizing the total length of the queues of the requests of diverse types is reduced to some problem of fractional-linear programming. The simulation models of the investigated system are constructed. The experiments, confirming the adequacy of the numerical results, have been carried out.
The Discrete Frequency Responses of Continuous Linear Systems
34-41
10.1615/JAutomatInfScien.v47.i9.40
Nikolay A.
Balonin
Saint-Petersburg State University of Aerospace Instrumentation (Russia)
Victor S.
Suzdal
Institute for Scintillation Materials of National Academy of Sciences of Ukraine, Kharkov
Alexander V.
Sobolev
Institute for Scintillation Materials of National Academy of Sciences of Ukraine, Kharkov
continuous linear systems
discrete frequency responses
finite time interval
convolution operator
optimal control problems
One aspect of linear dynamical system theory with the study of the spectral responses of the convolution operator on a finite time interval is considered. The practical significance of the result is that singular functions of the convolution operator have extreme properties and may be useful for solving optimal control problems.
Implementation of the Finite Element Method with Optimal Choice of Basic Functions for Dirichlet Problem for Poisson Equation
42-62
10.1615/JAutomatInfScien.v47.i9.50
Oleg N.
Lytvyn
Ukrainian Engineering and Pedagogical Academy, Kharkov
Konstantin V.
Nosov
V.N. Karazin Kharkov National University, Kharkov
Tatyana A.
Baranova
National Technical University "Kharkov Polytechnic Institute", Kharkov
finite element method
boundary value problem
Dirichlet problem
Poisson equation
The paper deals with the scheme of the finite element method with the choice of basic functions for elliptic boundary value problem. The main feature of this scheme is that the basic functions forming an approximate solution are not fixed in advance but should be calculated along with the values of node parameters. Computational experiment demonstrated that the scheme had a much higher accuracy compared with conventional schemes for which the basic functions are fixed.
Numerical Method of Integrating the Variational Equations for Cauchy Problem Based on Differential Transformations
63-75
10.1615/JAutomatInfScien.v47.i9.60
Mikhail Yu.
Rakushev
Ivan Chernyakhovsky National University of Defence of Ukraine, Kiev
variational equations
Cauchy problem
ordinary differential equations
differential transformation.
The paper presents the method for developing computational schemes of integration of the variational equations for Cauchy problem written for the system of ordinary differential equations. In this method obtaining all elements of the variational equations is implemented without analytical process of determining the partial derivatives of the functions which are the part of the right-hand side of the initial system of differential equations. The method is based on the differential transformations.
Uniform Sampling of Fundamental Simplexes as Sets of Players' Mixed Strategies in the Finite Noncooperative Game for Finding Equilibrium Situations with Possible Concessions
76-85
10.1615/JAutomatInfScien.v47.i9.70
Vadim V.
Romanuke
Khmelnitskiy National University, Khmelnitskiy
uniform sampling
fundamental simplex
players' mixed strategies
finite noncooperative game.
A method is suggested for the uniform sampling of fundamental simplexes as the sets of players' mixed strategies in the finite noncooperative game for its approximate solution. This solution is treated in the sense of equilibrium situations with possible concessions as Nash equilibrium situations are not necessarily to be on a finite simplex lattice. The sampling conditions assume that by changing minimally a situation over nodes of the lattice the players' payoff varies no greater than within its constant value. Building a simplex lattice of the player's mixed strategies set is fulfilled by a cyclic descent from the first pure strategy down to the last one. Retrieval of concession-equilibrium situations can be sped up by parallelizing of arrays multiplication when calculating the expected payoffs.