Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
44
11
2012
Self-intersection of the Phase Trajectories as a Measure of the Embedding Dimension of Chaotic Attractors. Part II
1-9
10.1615/JAutomatInfScien.v44.i11.10
Victor G.
Gorodetskyi
National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute", Kiev
Nikolay P.
Osadchuk
National Technical University of Ukraine "Kiev Polytechnic Institute"
embedding dimension
chaotic attractor
time series
high-dimensional system
integral curves.
This paper considers the problem of determining the embedding dimension in the reconstruction of a dynamical system using one observable variable. The proposed algorithm is based on the search for possible self-intersections of integral curves. The method was tested on time series with a noise, on real data on solar activity, on high-dimensional systems. An analysis of the possibility of applying this algorithm to estimate the embedding dimension is given for systems of different type.
The Estimation Method of Time-varying Parameters of Regression Models
10-28
10.1615/JAutomatInfScien.v44.i11.20
Arnold S.
Korkhin
National Mining University, Dnepropetrovsk
regression model
time-varying parameter
parameters estimation method
a priori information
computer experiment.
The basis of this method is a two-criterion problem of estimating the variable parameters of a linear regression. It allows to estimate the parameters, using sufficiently limited a priori information. The properties of the obtained estimates has been studied. The results of computer experiment, that have showed the efficiency of the proposed method, are given.
Quasioptimal Strategies in Differential Pursuit-evasion Games on a Plane
29-44
10.1615/JAutomatInfScien.v44.i11.30
Sergey V.
Pashko
Institute of Software Systems of National Academy of Sciences of Ukraine, Kiev
quasioptimal strategy
pursuit game
game value
pursuit strategy
payoff function.
The paper is concerned with differential pursuit-evasion games on a plane in which several players chase one. Quasioptimal strategies of players are defined and investigated. The inequalities which specify the sets of such strategies are derived. For the known strategies the conditions under which they are quasioptimal are found. The problems of choosing the best strategy from the set of quasioptimal are considered.
Optimal Approximate Algorithm for Reoptimization of Strict Constraint Satisfaction Problems
45-54
10.1615/JAutomatInfScien.v44.i11.40
Victor A.
Mikhailyuk
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
optimal approximate algorithm
approximation ratio
integrality gap on linear relaxation
hierarchy of relaxation
unique game problem.
With the unique games conjecture (UGC) held there exists the optimal approximate algorithm for reoptimization of strict constraint satisfaction problems (under insertion of any constraint). The approximation ratio of this algorithm depends on the integrality gap on linear relaxation of the original problem.
Numerical Solution of Optimal Control Problems of Nonlinear Dynamical Systems
55-69
10.1615/JAutomatInfScien.v44.i11.50
Anar Beybala ogly
Rahimov
Institute of Cybernetics of National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
optimal control problems
ordinary differential equations
piecewise constant
piecewise linear and piecewise-defined controls
analytical formulas of the functional gradient
optimization.
A numerical method for solving the optimal control problems for objects that are described by the system of nonlinear ordinary differential equations in the class of piecewise constant, piecewise linear and piecewise-defined controls, is proposed. In problems piecewise constant values of the coefficients of the formulas of control are optimized, and, what is more important, the boundaries of the constancy intervals of these values are optimized. The analytical formulas of the functional gradient by the parameters, which are optimized, are obtained. The functional gradient formulas, obtained for the initial continuous and appropriate discretized problems of optimal control in the class of piecewise constant controls, were compared. Numerical results are presented on the example of solving model problems.
Localized Wave Structures in Nonequilibrium Media
70-80
10.1615/JAutomatInfScien.v44.i11.60
Vyacheslav A.
Danylenko
S.I. Subbotin Institute of Geophysics of the National Academy of Sciences of Ukraine, Kiev
Sergey I.
Skuratovskiy
O.Ya. Usikov Institute for Radio Physics and Electronics, National Academy of Sciences of Ukraine, 12 Academician Proskura St., Kharkiv 61085, Ukraine
wave modes
one-dimensional system
three-dimensional phase state
wave solution
chaotic attractors.
We investigate the wave modes to a mathematical model for nonequilibrium medium. This model is written in the form of one-dimensional system of hydrodynamic type with the nonlocal dynamical equation of state. Using the methods of qualitative analysis it is shown that the three-dimensional phase space of the dynamical system describing the wave solutions of the model contains limit cycles of different multiplicity, heteroclinic and homoclinic loops as well as chaotic attractors.
The Nineteenth International Conference on Automatic Control "Avtomatikaâˆ’2012"
81-82
10.1615/JAutomatInfScien.v44.i11.70
Anatoliy P.
Ladanyuk
National University of Food Technologies, Kiev
Dmitriy V.
Lebedev
International Research and Training Center of Information Technologies and Systems of National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kyiv
International conferences on automatic control are held annually, initiated by Ukrainian association on automatic control (UAAC) and dated back to 1994.