Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
43
8
2011
Identification Problems of Linear Stationary Systems. Part I. Prony's Method
1-18
Vladimir B.
Larin
S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Alexander S.
Apostolyuk
National Technical University of Ukraine "Kiev Polytechnical Institute", Kiev, Ukraine
The survey of algorithms of solving of one of the simplest identification problems, which however has numerous applications, namely, the problem of determination of parameters of linear stationary system with continuous time by results of registration in discrete instants of time of transient process in this system is presented. We assume that the order of the system is known. Registration error is modeled by means of account of only fixed number of significant digits after decimal point. The considered algorithms are based on the idea of the Prony’s method about decomposition of the general identification problem to the problem of determination of exponent powers and subsequent finding of amplitudes of the corresponding modes. We note that according to the Prony’s method and the method of matrix pencils decomposition is realized by means of transition from the system with continuous time to the corresponding system with discrete time. Subsequent (inversed) transition from the system with discrete time to the system with continuous one in its turn can cause the additional errors of parameters estimates of initial system with continuous time.
To the Construction of Mathematical Models for Quasilinear Discretely Observed Distributed Space-Time Systems
19-32
Vladimir Antonovich
Stoyan
Kyiv National Taras Shevchenko University, Kyiv, Ukraine
Dmitriy A.
Golodiuk
Kiev National Taras Shevchenko University, Ukraine
The paper is focused on the dynamics of distributed space-time process which is discretely observed at the input and continuously observed at the output. The algorithms of linear, nonlinear and approximate identification of integral model of this process are proposed. The conditions of accuracy and uniqueness of existence of approximate solution are determined.
Necessary Condition for the Problem of Identification for One-Dimensional Nonlinear Stationary Equation of Quasioptics
33-45
Natik S.
Ibrahimov
Baku State University (Azerbaijan)
We investigate the identification problem for one-dimensional stationary equation of quasioptics on determination of quadrically summable coefficients, when nonlinear part of the equation contains only imaginary coefficient. Here we found formula for gradient of the functional, constructed by the final observation and ascertained the necessary condition of variational inequality type. We proved theorem of existence and uniqueness of solution of the direct problem.
Approach to the Priorities of Alternatives Determination for Multicriterion Selection Problems
46-50
Nikolay N.
Malyar
Uzhgorod National University, Ukraine
The approach to the alternative priorities determination for multicriteria problems of selecting high dimension has been proposed. This approach is based on the idea of maximal eigenvalue and the corresponding eigenvector for decision matrix.
Attainability of Optimal Solutions of Linear Problem of Multicriteria Optimization with Alternative Criteria in Transitive Subordination
51-55
Andrey Yu.
Brila
Uzhgorod National University, Ukraine
We consider techniques of determination of attainable optimal solutions of linear multicriteria optimization with alternative criteria in transitive subordination. The case, when between criteria there is certain dependence, which affects their selection on problem solving, is under investigation. For one particle transitive subordination we consider the problem of selection of sequence of criteria, which corresponds to lexicographically most optimal value of the objective function, constructed on the basis of this sequence.
Spectral Methods of Solving the Problems of Computer Steganography
56-75
Natalya V.
Koshkina
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
Valeriy K.
Zadiraka
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
A generalized model of the steganosystems functioning is presented and the basic principles of their construction are described. Various examples of application of the apparatus of the spectral analysis of signals and images for solving problems of computer steganography are given.
Generation of Random Numbers by Means of Optical Manipulator
76-80
Rostislav M.
Mikhersky
Krimea Branch of Europian University, Simferopol, Ukraine
Oleg I.
Popov
Krimea Branch of Europian University, Simferopol, Ukraine
The new way of random numbers generation through optical manipulator "mouse" is proposed. It is shown that in definite specially created circumstances optical manipulator can become an effective source of entropy in the cryptographically protected information systems. The speed of entropy generation in such sources can achieve 971 bit/sec.