Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
38
5
2006
On Structure of the Positional Absorption Set in the Game Problem of Pointing at a Target
1-5
10.1615/J Automat Inf Scien.v38.i5.10
Yuriy V.
Averbukh
Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russia
Properties of the positional absorption set in the problem of pointing a conflictively controlled system at a set are studied. It is demonstrated, that sections of the positional absorption set in a general case depend on time discontinuously and can be disconnected even for a connected goal set.
On Homogenization of Problems of Optimal Control. Part I. Analysis of Existing Approaches
6-22
10.1615/J Automat Inf Scien.v38.i5.20
Peter I.
Kogut
Oles Honchar Dnepropetrovsk National University
Victor N.
Mizernyi
Vinnitsa National Technical University, Ukraine
Tatyana N.
Rudyanova
Dnepropetrovsk State Financial and Economic Institute, Ukraine
We adduce results of qualitative comparison of existing approaches for solving the problem of averaging optimal control problems of systems with distributed parameters, which mathematical models depend on small parameter ε. Illustration of basic statements is supported by model examples.
Method of Solving Nonlinear Programming Using Variable Dimension Basis
23-33
10.1615/J Automat Inf Scien.v38.i5.30
Yuriy D.
Shcherbashin
National Technical University of Ukraine "Kiev Polytechnical Institute", Ukraine
Consideration is given to approximation programming method with gradually increasing/decreasing basis dimension. If the solution is found in the vertex of limiting polyhedron, i.e., on the boundary of intersection of
n-limiting hyperplane (n — dimension of space of searched variables), then the basis dimension reaches n; if the solution is on the faces or edges of limiting polyhedron, then the basis dimension decreases. With the solution found inside the admissible domain, then the basis dimension is zero and
X-trace on the last steps corresponds to the fastest descent (ascent) algorithm. The other feature of the method is the application of quadratic approximation of discrepancy Δ φi (X) variation along admissible appropriate direction — ray σ — linear combination of edges of current basis cone. The quadratic approximation method enables us to increase the step length in comparison with the simplest methods of approximation programming.
Solving of Some Problems of Combinatorial Optimization on Arrangements and Permutations of Game Type
34-45
10.1615/J Automat Inf Scien.v38.i5.40
Natalya Yu.
Ustian
Limited Partnership "SimCorp Ukraina", Poltava, Ukraine
Oleg A.
Emets
Poltava Consumer Cooperation University of Ukraine, Ukraine
We construct and investigate mathematical models of optimization problems on arrangements and permutations of game type, for which both players have combinatorial restrictions for use of their strategies. For problems of 2 × n and 2 × m dimension modified graphical method is suggested.
Mathematical Modeling of Processes of Filtration Consolidation with Accounting Relaxation Phenomena
46-55
10.1615/J Automat Inf Scien.v38.i5.50
Vladimir M.
Bulavatskiy
V. M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine
We construct mathematical model of filtration consolidation of massif located on impermeable basis under the condition of saturation by brine and with taking into account of relaxation character of filtration and diffusion processes. The corresponding nonlinear boundary-value problem is stated, numerical algorithm of its solving is formulated within the framework of exact and approximate models of consolidation, results of numerical realization of the algorithm are adduced.
On Mathematical Foundations of Functioning of Computer System of Optimal Control of a Trawler. Part I
56-64
10.1615/J Automat Inf Scien.v38.i5.60
Victor I.
Musurivskiy
Chernovtsy Yu. Fedkovich National University; and West-Ukrainian Economic and Law University, Chernovtsy, Ukraine
Formulation of problem of optimal control of a trawler described as a system with two degrees of freedom, is considered. Equations of motion of the system are Lagrange equations of the second kind. Problems solved by the Pontryagin maximum principle are formulated. In such formulations this principle plays the role of an economic-mathematical method. These problems demand creation of a decision-making system.
Adaptive Filtration with Constraints on Estimated Parameters
65-80
10.1615/J Automat Inf Scien.v38.i5.70
Vladimir N.
Podladchikov
Institute of Applied Systems Analysis of National Technical University of Ukraine "Kiev Polytechnical Institute"
Nina A.
Naroditskaya
Institute of Applied Systems Analysis of National Technical University of Ukraine "Kiev Polytechnical Institute", Ukraine
Elena V.
Podladchikova
Royal Observatory of Belgium, Brussels, Belgium
The paper introduces a new procedure for solving parameter identification problem with constraints on estimated parameters based on analysis of statistical characteristics of suboptimal finite memory filter discrepancy. We introduce equality type linear constraints on estimating the mathematical expectation of measurement noise and analyze accuracy of estimates obtained with and without these constraints. Consideration is given to applicability of proposed procedure to Sun heliograms analysis, efficiency of this application being shown.