Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
42
9
2010
Optimization of Transient Processes Characteristics of "Direct" Automatic Regulation Systems with the Poisson Perturbations
1-14
Evgeniy V.
Yasinskyy
Graduate Centre for Applied Psychology, Athabasca University, Edmonton (Canada)
Andrey Ya.
Dovgun
Bukovinskaya State Financial Academy, Chernovtsy, Ukraine
The conditions of asymptotic stability are obtained and qualitative characteristics of trivial solution for the system of nonlinear stochastic differential equations with Poisson perturbations are constructed. The absolute stability criterion in root-mean square sense of trivial solution for the systems of "direct" automatic regulation with Poisson perturbations is proved.
Minimization of Variance for Multidimensional Processes with Multirate Sampling for Models in Space of States with Delay
15-24
Victor D.
Romanenko
Educational-Scientific Complex of Institute
for Applied System Analysis of National
Technical University of Ukraine "Igor
Sikorsky Kiev Polytechnic Institute", Kiev
Alexey A.
Reutov
Applied Systems Analysis of National Technical University of Ukraine "Kiev Polytechnic Institute", Kiev, Ukraine; University of Warsaw, Warsaw (Poland)
We developed the method of optimal prediction of the vector of process state at the instant of delay by the control vector with further synthesis of control system for minimization of the generalized variance of the process for vectors and perturbations sampling with small periods and state control vectors discretization and evaluation with large sampling periods. Development of the prediction function is done on the basis of the Diophantine equations with respect to matrix polynomials.
Identification of Stationary Linear Systems by Irregular Measurements
25-35
Alexander S.
Apostolyuk
National Technical University of Ukraine "Kiev Polytechnical Institute", Kiev, Ukraine
Vladimir B.
Larin
S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The problem of identification of stationary linear system by the data of irregular measurements of the transient process is considered. The proposed identification algorithm is based on the procedure of decomposition of the initial problem. The effectiveness of the algorithm is demonstrated by an example.
Analysis of the Problem of Parametric Identification of Nonlinear Automata over Finite Ring
36-41
Vladimir G.
Skobelev
Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine
For the Mealy and Moore automata over finite associative-commutative ring with unit, which transition function is defined by means of nonlinear equations of the second order, and output function is correspondingly linear and affine mapping, we solved problem of parametric identification. Parameters, which can be easily identified, are detected, as well as parameters, which identification is not simple. It was ascertained that the property "to be reversible automata" does not affect complexity of solving the problem of parametric identification of the investigated models.
The Optimal Control Problem of Monocycle Biological Cells Aggregation
42-52
Vitally V.
Akimenko
Eastern-Ukrainian National University, Lugansk; and Kiev National Taras Shevchenko University, Ukraine
Yuriy V.
Zagorodniy
Kiev National Taras Shevchenko University, Ukraine
Viktoriya V.
Romanenko
Kiev National Taras Shevchenko University, Ukraine
The model of optimum control of monocycle cells aggregation in the set of piece-wise constant control functions is considered. The explicit analytic form of solution of the optimum control problem for criteria when cells density attains the required level is found. The numerical computation of dynamics of monocycle cells aggregation for control functions optimal values for three different kinds of objective function of biological cells distribution is performed.
Mathematical Modeling of Complex Social Economic Objects Based on Analogies with Physical Fractals
53-67
Yaroslav I.
Vyklyuk
Bukovina University, doctorant of National University “Lvovskaya Politekhnika”, Ukraine
The attributive and structural analogy is established between physical fractals and social economic systems. The algorithm of modeling the dynamics of social economic system development is synthesized. The mechanism of stagnation occurrence and system self-organization in the evolution process is studied. The functional analogy between the crystal entropy and the average level of system competition is established. The phenomenon of the second type phase transition under the change of fractal symmetry is studied and substantiated.
On the Probability Estimate of the Insurance Company Bankruptcy in the Model with Stochastic Premiums and Claims and the Opportunity to Invest in Financial (B, S)-market
68-80
Tatyana V.
Zhmykhova
Donbass National Academy of Construction and Architecture, Makeyevka, Ukraine
Boris V.
Bondarev
Donetsk National University, Ukraine
Artem V.
Baev
Donetsk National University, Ukraine
The mathematical model of the insurance company working on financial (B, S)-market is analyzed. The share price is described by Samuelsson model and the model, where Ornstein–Uhlenbeck process is the basic one for the description of the share price. The classical risk model is generalized, where the process of premiums and claims is stochastic. Power estimate of the insurance company bankruptcy probability depending on initial capital is constructed and the program control to minimize this probability estimate is found.