Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
34
5
2002
Evolutional Processes in Parametrically Modulated System of Linear Oscillators under Action of External Forces. Part I. System Analysis of Force Structure
13
Yuriy I.
Samoylenko
Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv
Alexey A.
Loginov
Institute of Space Research of National Academy of Sciences of Ukraine and National Space Agency of Ukraine, Ukraine
Evolutional processes caused by both parametrical and non-parametrical resonance control influence on a system of linear oscillators are studied. On the basis of the Bogolyubov averaging method, a vector differential equation with constant matrix coefficients, that describes dependence of oscillation amplitude on the "slow" time, is derived. Under the condition, that direct parametric resonances are absent in the first order of small parameter, wide possibilities for structure synthesis offerees in evolutional dynamics are demonstrated.
Optimal Perturbation of Pseudoinverse and Projection Matrices in the Problems of Linear Systems Synthesis
11
Sergey B.
Bublik
Kyiv National Taras Shevchenko University, Ukraine
Nikolay Fedorovich
Kirichenko
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kyiv
The problem of optimal synthesis of matrices in the linear algebraic systems with some criteria of quality is investigated for the purpose of application to formulation and research of problems of optimal distribution of controlling actions in the linear systems with discrete argument and boundary conditions. The necessary optimality conditions of discrepancy, norms of the principal solution and quantity of controlling actions both for a system of linear algebraic equations and boundary value problem based on general solving systems of linear algebraic equations, the general solving the control problem for linear discrete systems with boundary conditions as well as direct and reverse Greville formulas are formulated. The results of theory of pseudoinverse and projection matrices perturbation are employed for formulating conditions for optimal synthesis of matrices.
On Symmetrization of a Two-Point Boundary Problem
7
Vladimir B.
Larin
S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
We consider a two-point boundary-value problem with non-separated boundary conditions for a homogeneous Hamiltonian system of ordinary differential equations. We propose the algorithm of factorization of the fundamental matrix of this system which is concerned with construction of a solution of the algebraic Riccati equation both for the stationary and non-stationary systems. This factorization results in the matrix which symmetrizes the relationships connecting the values of the phase vector at the beginning and end of the interval. This, in its turn, improves the conditionality of the linear system of equations which define the initial conditions.
Determination of the Amplitude-Frequency Characteristic of the New Roller Damper for Forced Oscillations
8
Victor P.
Legeza
Ukrainian State University of Food Technologies and National University of Life and Environmental Sciences of Ukraine, Kiev
We consider forced oscillations of a damping system of two rigid bodies "heavy homogeneous ball in a spherical groove of a carrying moving body" under the external harmonic excitation. We found the frequency and the period of natural oscillations for the center of mass of the heavy ball in the immovable spherical groove. On the basis of the Duffing method we obtained the amplitude-frequency characteristic of the considered nonlinear mechanical system.
On the Problem about Complex Behavior of Dynamic Systems. Dynamics of Motion of a Vortex System in Ideal Liquid
12
Nikolay N.
Salnikov
Institute of Space Research of National Academy of Sciences of Ukraine and National Space Agensy of Ukraine, Kyiv, Ukraine
Yuriy P.
Ladikov-Roev
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
We consider dynamics of spatial motion of a system of thin closed vortex filaments in ideal liquid in context of the problem about simulation of complex behavior of systems. The motion equations are obtained under the condition that vortexes are under forces of arbitrary nature. In the case of motion of plane vortexes we obtain the general equations of dynamics in the Hamilton form. The known motion equations for co-axial vertex rings arise from the obtained equations as the particular case.
The Minimax Problems of Pointwise Observation for a Parabolic Boundary-Value Problem
16
Elena A.
Kapustyan
Kyiv National Taras Shevchenko University, Ukraine
Alexander G.
Nakonechnyi
Kiev National Taras Shevchenko University, Kiev
We consider the problems of minimax estimation of linear functionals from solutions of boundary-value problem for parabolic equations at pointwise observations. At first, the case of separate error restrictions is considered. Such problem is equivalent to the optimal pulse control problem. We obtain the results of minimax estimation in the problem when measurements are taken from some ellipsoid (a-minimax estimations). We suggest an approach for finding the approximating a0-minimax estimations which save a feature of the theorem about representation. One is to solve the problem of optimal control and the problem of one-dimensional optimization to find these estimations.