Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
32
12
2000
Some Constructions of Extension of Game Problems with Information Discrimination
1-11
Dmitriy V.
Khlopin
the Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russia
Alexander G.
Chentsov
N.N. Krasovsky Institute of Mathematics
and Mechanics of Ural Branch of Russian
Academy of Sciences, Ural Federal
University, Ekaterinburg
The extension of game's problem on maximin is constructed, in which one of the players − participants chooses a set from the given family, and the other selects an element from the specified set. The construction of extension uses embedding family of sets in compact space with Hausdorff metrics. The property having sense of stability of a generalized game problem with perturbation of criterion of quality is established. The applications to game problems of program control used in constructions of solution of differential games are considered.
On Synthesis of Stabilizing Controllers Using Linear Matrix Inequalities
12-17
Vladimir B.
Larin
S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Algorithm of synthesis of the stabilizing controllers is proposed. The algorithm is based on the linear matrix inequalities. The algorithm includes a procedure of minimization of controller norm. Problems of synthesis for stationary systems with continuous and discrete time are considered in detail. The algorithm is generalized on the case of a periodic system with uncertain parameters.
Linear Differential Games with Simple Matrices and Integral Constraints
18-22
Irina L.
Ryzhkova
Research and Training Complex "Institute of Applied System Analysis" of National Academy of Sciences of Ukraine and Ministry of Education of Ukraine, Kyiv, Ukraine
We consider problems of keeping and ending with fixed finish time in linear differential games with constant matrices and integral constraints for player's control. In contrast to games with an arbitrary matrix we solve completely the keeping problem and under certain conditions − the pursuit problem. We have obtained the new theorems about an alternative.
Control of Pseudo-Hyperbolic Systems by Concentrated Impacts
23-36
Sergey I.
Lyashko
Kiev National Taras Shevchenko University, Kiev
Vladimir V.
Semenov
Kiev National Taras Shevchenko University, Kiev
Ivan I.
Lyashko
T. Shevchenko National University, Kiev, Ukraine
A problem of generalized control of system, described by the third initial boundary problem for pseudo hyperbolic equation is considered. Generalized solvability of initial boundary value problem by method of a priori inequalities in negative norms and controllability for system, when control is performed over concentrated impacts, which set right parts from some negative space is investigated.
Instability Region of Current Plasma of Denseness Variable Profile
37-42
Boris N.
Lyashenko
Ivan Franko Zhitomir Pedagogical University, Ukraine
The necessary condition of existence of unstable condition of plasma of the denseness variable profile are established. The algorithm of a surface construction of such plasma instability region is developed. The numerical example is presented.
Minimax Estimation for Solutions of Transmissions Problems for Elliptic Equations under Absence of Information about Conjugating Conditions
43-59
Yuriy K.
Podlipenko
Kyiv National Taras Shevchenko University, Kyiv, Ukraine
Amer Mansor
Dababneh
Belorussian State University of Transport, Gomel
The minimax estimations for functional from solutions of boundary problems, which describe transmissions for linear elliptic equations of the second order, are obtained on the basis of observations of the systems state. It is provided for the property that conjugating conditions are unknown and relative to right-hand parts of equations, boundary conditions and errors of measuring we know only that they belong to certain given sets. We find systems of integral-differential equations of a special type, which solutions are used for expression of the minimax estimates. Their unique solvability is proved.
Fuzzy Ellipsoidal State Observer of Reduced Order
60-68
Nataliya N.
Kussul
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
The problem of synthesis of fuzzy reduced order ellipsoidal state observer for multidimensional discrete dynamic systems is considered. Developed algorithms have robustness property, i.e. non-sensitivity to the violation of a priory suggestions about the system. Computer modeling of adaptive control system for spacecraft orientation confirms the effectiveness of developed algorithm.
Mean Square Approximation of Solutions of Stochastic Differential Equations Using Legendre's Polynomials
69-86
Dmitriy F.
Kuznetsov
St. Peterburg State Technical University, Russia
We consider approximation for iterated Stratonovich stochastic integrals using multiple Fourier series in terms of Legendre polynomials. We have obtained approximations of stochastic integrals of the multiplicity 1−5. We consider root-mean-square convergence of approximation of iterated stochastic integrals.
Asymptotic Solution of Control Problem of a Standard System with Variable Delay
87-92
Vitaliy P.
Joltikov
Odessa National I.I. Mechnikov University, Ukraine
Vladislav V.
Efendiev
European University, Uman
The study of real controlled processes based of the idealized mathematical models usually leads to the differential equations with small parameters. A choice of a specific asymptotic method of study depends on a structure of a differential equation which describes dynamics of a controlled object. Many properties of real objects are formed by the delay effect. Therefore, the asymptotic averaging of the standard systems with a variable delay is suggested.