Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
51
5
2019
On the Optimal Impulse Control in Descriptor Systems
1-15
10.1615/JAutomatInfScien.v51.i5.10
Larisa A.
Vlasenko
V. N. Karazin Kharkov National University, Ukraine
Anatoliy G.
Rutkas
Kharkov National University of Radio and Electronics, Kharkov
Valeriy V.
Semenets
Kharkov National University of Radio and Electronics, Kharkov
Arkadiy A.
Chikriy
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine
descriptor system
differential algebraic equation
quadratic performance functional
impulse intensities
moments of impulse application
optimal impulse control
adjoint state
two-point boundary value problem
radio technical filter
transient state
We study the optimal impulse control problem with the quadratic performance functional for a descriptor system. The system evolution is described by a linear differential-algebraic equation unsolved with respect to the derivative of the state. The system is controlled by changing the measurable control and the pure impulse control. The pure impulse control is characterized by impulse intensities and moments of impulse applications. The main restriction is that the characteristic matrix pencil corresponding to the state equation is regular. In terms of characteristic matrix pencil we establish the conditions for the existence and uniqueness of the optimal control and the corresponding optimal state. The optimal control and the optimal state are constructed by using the adjoint state which is a solution of the adjoint two-point boundary value problem. The results are illustrated by the example of descriptor system that describes transient states in a radio technical filter. For this system we consider the energetic performance functional with impulse intensities characterizing the energy of inertial elements and input voltage of the filter and also intensities and moments of impulse applications. Transient states under impulsive perturbations of currents and voltages are described by using the formula of constants variation for the impulsive descriptor system.
Computer Simulation Based on Non-local Model of the Dynamics of Convective Diffusion of Soluble Substances in the Underground Filtration Flow under Mass Exchange Conditions
16-29
10.1615/JAutomatInfScien.v51.i5.20
Vsevolod A.
Bohaienko
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
Vladimir M.
Bulavatskiy
V. M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine
dynamics of convective diffusion processes
steady-state plane-vertical groundwater filtration
mathematical modeling
fractional differential mathematical models
Caputo-Katugampola fractional derivative
nonlinear boundary value problem
finite-difference solutions
The paper deals with the problem of modeling the dynamics of locally nonequilibrium in time process of soluble substances convective diffusion under the conditions of flat-vertical steady-state groundwater filtration with free surface taking into account the presence of phase-to-phase mass transfer. The urgency of solving such problem is due, in particular, to the need for development of measures for soil flushing as well as desalination and purification of groundwater from pollutants. For mathematical modeling of the corresponding transfer process in media with a property of temporal nonlocality this paper used the apparatus of fractional-order integro-differentiation. The corresponding nonlinear fractional differential model of the migration process has been developed using Caputo-Katugampola generalized fractional order derivative of a function with respect to another function which allows us in a sense to control the modeling process. In this model the nonequilibrium convection-diffusion process in a porous medium is considered under conditions of mass exchange. For the proposed mathematical model the formulation of the corresponding boundary value problem was carried out and the technique for its numerical solution was developed. This technique is based on a preliminary transition using the conformal mapping method from the physical How domain to the domain of complex potential which is canonical. The algorithm for approximate solution of the considered boundary value problem in the domain of complex potential is based on a linearized version of the locally one-dimensional difference scheme of A.A. Samarsky. The results of computer simulations demonstrate that the value of the exponent in the Caputo-Katugampola derivative significantly affects the simulation results giving both sub-diffusion and super-diffusion patterns of concentration fields distribution. Computational experiments also show that when mass exchange phenomenon is taken into account while modeling pollution propagation from water bodies to soil media it leads to a delay in the concentration front development in a liquid phase. The paper has drawn the conclusions regarding the influence of the mathematical model parameters on the resulting picture of concentration fields formation.
Computer Modeling of the System Pipeline-Liquid Behavior. Research and Estimate of the Effect of the Coriolis Forces on Liquid Motion in Pipeline for Different Ways of Fixing
30-37
10.1615/JAutomatInfScien.v51.i5.30
Valeriy V.
Gavrilenko
National Transport University, Kiev
Oleg S.
Limarchenko
Kiev National University, Kiev
Oxana P.
Kovalchuk
National Transport University, Kiev
pipe with flowing fluid
nonlinear vibrations of system
different ways of pipe fixing
nonlinear mechanisms
Coriolis forces
redistribution of the energy
One of the most important problems of science and technology is the study of the behavior of pipelines under transient liquid flow modes in vicinity of critical velocities of the fluid. Particular attention is paid to the behavior of the system on approaching the critical flow velocities when the loss of stability of the rectilinear shape of the pipeline occurs. This can lead to the destruction of the pipeline. Therefore, from the point of view of high costs of such objects and potential negative consequences in case of pipeline destruction, the question about the development of effective methods of mathematical modeling of the pipeline — liquid in the linear and nonlinear ranges of the system parameters arises. The problem of dynamics of pipe with a flowing fluid is considered. Vibrations of the system in the nonlinear range of disturbances are studied. For different ways of pipeline fixation, we perform the analysis of the effect of nonlinear mechanisms and the Coriolis forces on the redistribution of the energy between normal modes of the system oscillations. It is shown that according to their contribution the Coriolis forces dominate in the redistribution of the energy between normal modes of oscillations of the system. It is noted that under the presence of a free edge an integral effect of the Coriolis forces and nonlinear mechanisms is manifested maximally. The developed model is sufficiently universal and can be applied to study many application problems of pipeline dynamics in transient modes of motion. Important results are the analysis of the effect and nature of various nonlinear mechanisms, the study of different fluid flow modes, and the potential to use the flow law for damping oscillations.
Guaranteed Prediction Estimates of Solving Systems of Differential Equations with Gompertz Dynamics under Observations at Discrete Time Instants
38-53
10.1615/JAutomatInfScien.v51.i5.40
Alexander G.
Nakonechnyi
Kiev National Taras Shevchenko University, Kiev
Petr N.
Zinko
Kiev National Taras Shevchenko University, Kiev
Taras P.
Zinko
Kiev National Taras Shevchenko University,
Kiev
Yulia M.
Shevchuk
Kiev National Taras Shevchenko University, Kiev
systems of nonlinear differential equations
Gompertz dynamics
guaranteed prediction estimates
discrete observations
uncertainty
The mathematical model of information spread in a social medium is analyzed. It is assumed that in a sociocommunicative space there spread n types of information messages different in content. The number of individuals spreading one of the types of information messages is a key indicator of the model dynamics. Information messages spread through internal (interpersonal communication) and external (media influence) flows. The model is presented in the form of the system of n Gompertz nonlinear differential equations. It is appropriate to apply such models in practical problems of analyzing an information spread in a social medium dynamics of which is fast growing in time. Having a nonlinear right part such models claim to be an adequate representation of processes in a subject area. One of the practical important problems which occur while analyzing processes of information spread in a social medium is the problem of finding prediction estimates of such processes dynamics. For the systems of Gompertz differential equations this problem becomes nontrivial due to natural logarithms in the right-hand sides of these equations. The problem of finding the guaranteed prediction estimates of vectors is formulated. For a particular case of this problem with discrete observations there were proposed the efficient algorithms for finding guaranteed and approximate guaranteed prediction estimates of state and error vectors of prediction guaranteed estimates. As example there are presented results of finding the guaranteed prediction estimates of dynamics of mathematical model of one form information spread in a social medium. Results of numerical computer experiment demonstrate practical opportunities of this scheme. The proposed technique can be used for development of decision support systems for analyzing processes in sociocommunicative space.
Information Technology of Separating Hyperplanes Synthesis for Linear Classifiers
54-64
10.1615/JAutomatInfScien.v51.i5.50
Alexander V.
Barmak
Khmelnitskiy National University, Khmelnitskiy
Yuriy V.
Krak
Kiev National Taras Shevchenko University, V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
Eduard A.
Manziuk
Khmelnitskiy National University, Khmelnitskiy
Veda S.
Kasianiuk
Kiev National Taras Shevchenko University, Kiev
multidimensional scaling
multidimensional classification
data visualization
Information technology allowing one to implement the tasks of classification, clustering, studying the topology of the data of the information component is proposed. The multidimensional feature space is reduced to the visual presentation space to determine the information content of the data. Optimized reduction of the space dimension to two-dimensional one applying multidimensional scaling methods is used. Visual definition of grouping data allows separating areas to form. The next stage is visual limitation of categories of classes using graphic separators. To enable flexibility of nonlinear areas limitation a combination of linear ones is used, thereby forming a piecewise linear set with necessary degree of sampling. Using piecewise linear constraints allows us to implement projecting into original multidimensional feature space. Visual construction of restrictive separators makes it possible to consider tolerance fields of changing of features parameters, separation measure of classes, nonlinearity of data grouping. This is followed by reverse expansion of space with the projection of the separators into n -dimensional space with the separating hyperspace synthesis. Thus the limitative areas of hyperspace for the necessary categories of classes are formed. At the same time the visualization of classification process in a hyperspace is provided. The information technology base is the multidimensional space projection into visual (two-dimensional) space construction piecewise linear limiters of studied areas, subsequent limiters projecting into multidimensional space. Thus the information technology enables us to synthesize separating hyperplanes limiting categories of classes in multidimensional space. The technology application successive stages are described.
Improved Mathematical Model of Fluid Level Dynamics in a Drum-Type Steam Generator as a Controlled Object
65-74
10.1615/JAutomatInfScien.v51.i5.60
Alexander A.
Klymchuk
Odessa National Polytechnic University, Odessa
Vadim F.
Lozhechnikov
Odessa National Polytechnic University, Odessa
Vladislav S.
Mykhailenko
National University "Odessa Maritime Academy", Odessa
Nadezhda V.
Lozhechnikova
Odessa National Polytechnic University, Odessa
drum-type steam generator
steam line
heat generation in a combustion chamber
steam flow control valve
mathematical model
The features of mathematical modeling of the dynamic properties of the level of a steam-water mixture in a drum-type steam generator are considered. It is shown that boiling up of the steam-water mixture level in the drum-type steam generator, which is extremely unfavorable for automatic control system, is a consequence of occurrence of complex thermophysical processes and design features of the technological section. Therefore it is not appropriate to use mathematical models for modeling the level dynamics which do not take into account the effect of the accumulating and throttling properties of the steam line on the saturated vapor flow from the steam generator and the main disturbing action (steam consumption) is considered as an independent variable. The article proposes a linear mathematical model of the power supply section of the drum-type steam generator which takes into account the dynamic properties of the steam line connecting the steam generator with a consumer. The structural scheme analysis of the proposed mathematical model showed that between the drum-type steam generator and the steam line there is an inverse relationship with steam consumption. The negative nature of this connection explains the self-leveling associated with a change in the position of the steam flow control valve of heat generation in the combustion chamber. Accordingly, a change in the flow area of the turbine control valve, without changing the heat release by the heat load regulator in a combustion chamber or a nuclear reactor leads to a temporary change in steam consumption. This leads to less intense boiling up of the level and its transition to a new steady-state value. The level stabilization occurs below the initial value due to a brief disruption of the balance between the feed water supply to the steam generator and the steam extraction. Identified, as a result of solving the system of differential equations, peculiarities of the behavior of the steam- water mixture level make it possible to simulate more adequately the operation of existing and prospective power control systems for drum-type steam generators.