Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
41
11
2009
Invariant Sets of Nonlinear Discrete Systems with Bounded Disturbances and Control Problems
1-16
Boris T.
Polyak
Trapeznikov Institute of Control Problems of the Russian Academy of Sciences, Moscow, Russia
Vsevolod M.
Kuntsevich
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
The paper consists of two interdependent parts. In the first part we calculate the upper-bound estimates of invariant sets and their radii for the class of nonstationary linear discrete systems and certain nonlinear discrete systems under bounded disturbances with the given a priori set-values estimates. In the second part, based on the calculated upper-bound estimates of the radii of invariant sets, we synthesize the control that minimizes these estimates for the closed-loop systems with a feedback.
Differential Games of the Fractional Order with Separated Dynamics
17-27
Arkadiy A.
Chikriy
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine
Alexander G.
Chentsov
N.N. Krasovsky Institute of Mathematics
and Mechanics of Ural Branch of Russian
Academy of Sciences, Ural Federal
University, Ekaterinburg
Ivan I.
Matychyn
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine
Game approach problems for linear conflict controlled processes with fractional derivatives of arbitrary order are studied. The classical fractional Riemann-Liouville derivatives, regularized Dzhrbashyan-Nersesyan or Caputo derivatives as well as sequential Miller-Ross derivatives are considered. For the fixed controls of players, the solutions in the form of analogs of the Cauchy formula, with the use of the generalized matrix functions of Mittag-Leffler, are determined. The method of resolving functions is used as the basic one, which allows to obtain the sufficient conditions for the solvability of the approach problem in a guaranteed time. The results are illustrated by the model example of a game problem with separated motions of the fractional order π and e.
Mathematical Modeling of the Dynamics of Distributed Time-space Process of the Convective Diffusion of the Binary Mixture under Conditions of Mass Exchange
28-39
Vladimir M.
Bulavatskiy
V. M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine
There has been developed the asymptotics of the solution of two-dimensional boundary value problem of the convective diffusion of the binary mixture in the case of steady filtration in the doubly connected domain restricted by two equipotential lines under condition of convective mechanism of mass transfer domination over diffusive one and the high intensive mass exchange.
Polar Ecliptic Patrol for Investigation of the Sun and Solar Sources of Space Weather Monitoring
40-47
Vladimir D.
Kuznetsov
Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation of Russian Academy of Sciences, Troitsk, Moscow region, Russia
For study of solar activity and monitoring of solar sources of space weather we suggest usage of two small spacecrafts (SC) on inclined relative to ecliptic plane heliocentric orbits. The inclined orbits with approximate distance from the Sun 0.5 a.u. are formed as the result of gravity maneuvers near the Venus, which are performed with application of electric jet engine. Here the planes of orbits are inclined asunder relative to each other, and SC are distant on orbits for quarter of period. According to this orbital scheme from one of SC monitoring of the line Sun-Earth is provided continuously, and this monitoring is done from both SC in durable time. Polar domains of the Sun become accessible for monitoring, which are not well visible from ecliptic orbits of SC, as well as the reverse side of the Sun, which is invisible from the Earth. Multiposition local measurements make it possible to study properties of the solar wind and energetic particles in internal heliosphere.
The Modified Method of Design of One Class of Fuzzy Digital Controllers
48-59
Vladimir I.
Gostev
State University of Information and Communication Technologies of Ministry of Transport and Communication of Ukraine, Kiev, Ukraine
For the purpose of developing the method of designing of one class of fuzzy controllers, which is based on analytic expressions for the controlling actions on the output of fuzzy controller for different membership functions, the modified method, which significantly simplifies the design of one of three main blocks of a fuzzy controller, is represented
On Merton's Problem in the Case of Periodic Fast Oscillating Stochastic Coefficients
60-80
Boris V.
Bondarev
Donetsk National University, Ukraine
Sergey M.
Kozyr
Donetsk National University, Ukraine
Merton's problem of investor portfolio optimization with possibility of investments in risk and risk free assets and their partial consumption is considered. The integral functional of cost corresponds to behavior of investor averse to risk. To describe risk asset evolution Samuelson model with fast oscillating periodic stochastic perturbations is used. The interest rate is also periodic fast oscillating stochastic function.