Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
44
9
2012
Estimates of Stable Limit Cycles of Nonlinear Discrete Systems
1-10
Alexey V.
Kuntsevich
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kyiv
Vsevolod M.
Kuntsevich
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
For rather large family of autonomous nonlinear discrete systems the conditions of the existence of invariant sets (stable limit cycles) are found. The methods of determining the upper-bound estimates of limit cycles are proposed. Illustrative examples are given. The main attention is paid to the determining the radius of the estimate of a limit cycle, since it determines the maximum deviation of the system from the origin during the motion of the system on the limit cycle.
Self-intersections of the Phase Trajectories as a Measure of the Embedding Dimension of Chaotic Attractors. Part I
11-23
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"
The purpose of this study is to test the hypothesis about the possibility to use of self-intersection of the phase trajectories to determine the embedding dimension of chaotic attractors. An algorithm of finding possible intersections of integral curves is developed. The problem of the lack of information about the behavior of the trajectory between the points, obtained in the space on the basis of the observed time series, is solved by replacing the integral curve by a broken line.
Identification of Multivariable Systems Using Steady-state Mode Parameters
24-42
Vyacheslav F.
Gubarev
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
Sergey V.
Melnichuk
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev
The paper has developed the updated method for identification of multivariable linear systems described by the state space model using the approximate steady-state mode parameters which are defined by the integration of experimentally obtained output signals under the harmonic excitation on the input. The method allows one to update the model of dimension maximum permissible by stability condition to make it possible to approximate the real system output with accuracy consistent with errors in the obtained data.
Modification of Prony's Method in the Problem of Determining the Parameters of Sinusoids
43-50
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
A modification of Prony's method as applied to the problem of determining the parameters of sinusoids has been offered. On this basis, the appropriate algorithm of determining the estimates of parameters of sinusoids has been proposed. The proposed approach is less laborious since it is not related to the integration procedure of the system of differential equations. The efficiency of the presented algorithm has been shown by the examples.
General Scheme to Obtain Necessary Optimality Conditions for Continuous Optimal Set Partitioning Problems
51-65
Elena M.
Kiseleva
Oles Honchar Dnipro National University, Dnepr
Alexandra A.
Zhiltsova
Oles Honchar Dnepropetrovsk National University
Viktoriya A.
Stroyeva
Dneprodzerzhynsk State Technical University
General continuous deterministic multiproduct optimal set partitioning problems are formulated in terms of the set function theory. The problems with constraints in the form of inequalities and those with constraints in the form of both equalities and inequalities are considered. For these problems, the necessary optimality conditions are obtained both in the general and constructive form, which can be easily applied to the specific classes of problems. The theorems application is illustrated by example of deterministic multiproduct nonlinear optimal set partitioning problem with the subset center arrangement and constraints in the form of equalities and inequalities.
Compromise Method of Solving Constrained Optimization Problems
66-73
Albert N.
Voronin
National Aviation University, Kiev, Ukraine
The possibility of a compromise solution in constrained optimization problems is considered. The problem is that the resulting decision would reflect a compromise between the contradictory requirements of extremalization of the objective function and couplings satisfaction. For solving the considered problem the approach of multicriteria optimization with the use of a nonlinear scheme of compromises is chosen. A model example is given.
Necessary Optimality Conditions in a Discrete Control Problem with Nonlocal Boundary Conditions
74-83
Kamil Bayramali oglu
Mansimov
Institute of Cybernetics of National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
A problem of optimal control, described by the system of nonlinear difference equations with nonlocal boundary conditions, is considered. Using the modified procedure of the increment method we prove the necessary condition of optimality of the discrete Pontryagin maximum principle type. The case of degeneration of the discrete maximum principle is studied separately.