Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
34
11
2002
The Synthesis of Stabilizing Control of a Rigid Body with Attached Elastic Elements
10
Alexander M.
Kovalev
Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk, Ukraine
Alexander
Zuyev
Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine
Vladimir F.
Shcherbak
Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk, Ukraine
We consider the problem of synthesis of nonlinear control law for a simulated mechanical system, which consists of a rigid carrying body and attached to it flexible beams. The system performs planar motion under controlling moment of forces applied to the carrying body. For obtaining a mathematical model in the form of a system of ordinary differential equations we make use of the modal method of discretization. The motion equations are presented in the Euler-Lagrange form with infinite number of elastic coordinates and a variable, which characterizes orientation of the carrying body. In order to obtain the nonlinear system we found control in the form of feedback, which provides asymptotical stability of the equilibrium state relative to definite combinations of elastic coordinates and orientation of the carrying body. For investigation we applied the approach of the Lyapunov control functions relative to a part of variables. We proved the Lyapunov stability of the complete system with respect to all phase variables. The question about realization of the obtained feedback for additional measurements of relative shears of a beam was studied. We show observability of the investigated system for different modes of motion. The results of numerical simulation are adduced.
Representations of Solutions for Controlled Hybrid Systems
8
Vladimir M.
Marchenko
Byelorussian State Technological University, Minsk, Belarus
An integral representation of solutions expressed by means of solutions of boundary-value problems of corresponding conjugate system is obtained for linear nonstationary controlled hybrid systems, This formula is very similar to the well-known Cauchy one in linear system theory. The results obtained are adjusted for the case of linear stationary hybrid systems with control.
Influence of the Follower Force Orientation on Stability Domains of the Upper Equilibrium State of Inverted Double Pendulum
8
Leonid G.
Lobas
Kyiv Institute of Railway Transport, Ukraine
Lada L.
Lobas
Boston College, USA; and Karlov University, Prague, Czechia
Dependence of boundaries of domains of flatter and divergent instabilities on the asymmetry parameter of the follower force is established. A procedure of finding limits of applicability of the Euler static concept in the theory of stability of compressed elastic rods is suggested.
Control of the Telescope Mirror Geometry on the Basis of Solving the Inverse Problem
8
Lyubov V.
Maksymyuk
Institute of Space Research of National Academy of Sciences of Ukraine and National Space Agency of Ukraine, Kyiv, Ukraine
We propose the new method of control of geometry of the axis-symmetrically deformed mirror of the space telescope on the basis of solving the inverse problem of the theory of thin shells. Recovering of the shape of the adaptive mirror is realized by normal forces. We state the problem of the inverse problem and show its uniqueness. Algorithm peculiarities of the numerical solution of the inverse problem, which are caused by loss of accuracy on numerical differentiation, are ascertained. We present numerical results of solving of agreed problems according to the scheme "direct problem — inverse problem — direct problem" and give their analysis. We discover high sensitivity of the solution of the inverse problem relative to adequacy of the mathematical model of the mirror, smoothness of input data and neglect of tangent displacements. It was shown that in the case of deformation of the thin mirror by gravity forces neglect of geometric nonlinearity results in overcompensation of deflection by significant from point of view of optics value.
Analytical, Geometrical and Numerical Investigations of a Class of Multicriteria Continuous Problems of Set Partitioning
12
Natalya K.
Vasilyeva
Dnepropetrovsk National University, Ukraine
We consider multiple-objective problems of set partitioning with integral criteria of Manhattan and Chebyshev metrics. We obtained the conditions of optimality by Slater and Pareto for these problems. Connections of effective, weakly and strongly effective solutions with geometric configurations of partitioning boundaries were established. We suggested the algorithm of searching optimal by Slater and Pareto solutions of the problems under consideration.
On Application of Informational Criteria in Problems of Control of Nonlinear Stochastic Systems
6
Sergey V.
Sokolov
Rostov State University of Railway Transport (Russia)
Vladimir A.
Pogorelov
Rostov Military Institute of Rocket Forces, Rostov-on-Don, Russia
The problem of optimal control of nonlinear stochastic systems is solved on the basis of informational criteria. The dynamic target control is synthesized on the example of applying Fischer and Shannon criteria. Numerical results confirming validity of the conclusion made on the efficiency of practical use of this solution are obtained.
The Scheme of Sliding Examination for Optimal Set Features Determination in Discriminant Analysis Problem
11
Alexander P.
Sarychev
Institute of Technical Mechanics of National Academy of Sciences of Ukraine and National Space Agency of Ukraine, Dnepropetrovsk, Ukraine
It is analytically shown that the traditional scheme of sliding examination allows one to solve the discriminant analysis problem stated in a broad sense on final samples of observations. The existence of optimal set of features is shown which corresponds to a maximum of mathematical expectation of offered generalized distance between observations from two parent populations. It is analytically shown that the parameters of parent population and sample size influence complexity of optimal discriminator. The conditions are found at which the optimal discriminator becomes reduced.