Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
51
4
2019
Method for Prediction of Space Vehicle Motion Based on the Multidimensional Differential-Taylor Transformations
1-11
Mikhail Yu.
Rakushev
Ivan Chernyakhovsky National University of Defence of Ukraine, Kiev
A numerical-analytical method for integrating the differential equation of spacecraft motion, developed on the basis of multidimensional differential-Taylor transformations, is presented. A distinctive feature of the proposed method is the calculation of accelerations in the differential equation of spacecraft motion based on differential-Taylor transformations of different dimensions, namely: accelerations produced by conservative forces (geopotential) based on two-dimensional differential-Taylor transformations, and accelerations produced by non conservative forces (atmospheric drag, gravity of the Moon and Sun, moveable centrifugal force, Coriolis inertia force) − based on one-dimensional differential-Taylor transformations. Such approach reduces the necessary number of analytical calculations when specifying the differential equation of spacecraft motion, ensures a methodical unification of the process of developing procedures for predicting spacecraft motion. The results of comparing the computational complexity of the proposed method of integration with a well-known method based on one-dimensional differential-Taylor transformations are presented.
The Development of Application to Software Origin Pro for Informational Analysis and Forecast of Forest Fire Danger Caused by Thunderstorm Activity
12-23
Nikolay V.
Baranovskiy
National Research Tomsk Polytechnic University, Tomsk, Russia
Forest fires occur due to a variety of natural and man-made causes. The main natural cause of forest fires is thunderstorm activity, namely, the impact of cloud-to-ground lightning discharges. It is known that for the analysis of spatial information geographic information systems are widely used. The purpose of this work is to demonstrate the capabilities of our own program code interacting with the Origin Pro software for geoinformational analysis of forest fires arising due to thunderstorm activity. There are various ways to predict and assess forest fire danger from thunderstorms. In this work the approach of a deterministic-probabilistic forecast of forest fire danger is used. In the process of research our own program code has been developed for assessing forest fire danger and its characteristics on the example of the Timiryazevskiy forestry of Tomsk region. The application works in dialog mode. The Origin Pro software is used for visualization and additional advanced data analysis by the parameters of forest fire danger. Data processing for thunderstorm activity and meteorological parameters with reference to probabilistic assessment of forest fire danger is demonstrated.
Method of Resolving Functions in the Group Pursuit Problem with a Terminal Pay Off Function and Integral Constraints on Controls
24-42
Iosif S.
Rappoport
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
A method is proposed for solving game dynamics problems with a terminal pay off function and integral constraints on controls which consists in systematical using the ideas of Fenhel−Moreau as applied to the general scheme of resolving functions method. The essence of the proposed method lies in the fact that the resolving function can be expressed in terms of the function conjugate to the pay off function and using the involute of the conjugation operator for a convex closed function to obtain a guaranteed estimate of the terminal value of the pay off function which is represented by the paying off value at the initial time instant and the integral of the resolving function. The main feature of the method is the cumulative principle used in the current summation of the resolving function for estimating the game quality until a certain threshold value is reached. The paper considers linear differential games of group pursuit with a terminal pay off function and integral constraints on controls. Sufficient conditions for the game completion in a finite guaranteed time in a class of quasi-strategies are formulated. Two schemes of the resolving functions method are proposed that ensure without additional assumptions the game completion in the final guaranteed time in the class of stroboscopic strategies. The results of comparing the guaranteed times of different schemes of the resolving functions method are presented.
Approximative Properties of the Generalized Poissin Integrals on the Classes of Functions Determined by a Modulus of Continuity
43-54
Yuriy I.
Kharkevych
Lesya Ukrainka Eastern European National University, Lutsk
One of the most important problems of applied mathematics is to study various problems of natural science which ultimately lead to compilation of mathematical models of phenomena under study. Moreover these mathematical models will be of practical interest if and only if they adequately reflect real situations. Very often the objects studied are extremely complex. In such cases some other method can be a real find for obtaining an additional information about this quantity, allowing its solution to be obtained at least approximately. In this case it is advisable to apply the methods and approaches of the theory of function approximation, namely, the asymptotic estimates. The theory of functions approximation is important because it gives general grounds for practical calculation of functions for the approximate replacement of complex functions by simpler ones. In this case an important role is played by the modulus of continuity which characterizes the maximum absolute increment of the function studied between the points of the definition domain. Also of importance are the classes of functions defined by the modulus of continuity, in particular, the Hölder classes. This paper studies the problem of finding the exact upper bound of deviation of functions classes that are determined by the first order modulus of continuity from their generalized Poisson integrals. In a particular case there were obtained the asymptotic equalities for approximating functions of Hölder classes by their generalized Poisson integrals. Thereby it was shown that a transition from classes Hω to more "susceptible" Hölder classes of functions H1 provided more qualitative solution of Kolmogorov−Nikolskii problem for generalized Poisson integrals in a uniform metric that has a direct application in mathematical modeling and mathematical formalizations in certain types of problems in a game theory.
Computational Complexities of Modeling of Dynamical Systems with Anticipation
55-65
S. V.
Lazarenko
Institute for Applied System Analysis of
National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic
Institute", Kiev
Alexander S.
Makarenko
Educational-Scientific Complex of Institute
for Applied System Analysis of National
Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute", Kiev
The concept of anticipation foresees the dependence of future states not only on the past but also on their future states. One of the main reasons causing urgency of the study of anticipatory systems is the ultimate resource capacity of the problem of modeling of the systems with multiple potential scenarios since anticipatory systems often provide for multivalued solutions. Not great number of publications in this field of computer science is also often caused by ill-posed problem statements due to the existence of several potential solutions. In that way, the systems with anticipation represent a new direction in cybernetics and the models based on anticipation can formally describe a great number of existing systems and processes with higher accuracy in comparison with classical models with delay. We consider the following nonlinear discrete dynamical systems with strong anticipation, where future states can be represented by an explicit dependence on the past ones by means of the Hutchinson operator. The evolution of such dynamical systems is carried out in the Hausdorff metric space. We consider the fundamental problem of such systems modeling, i.e., the volume of use of computation resources. A number of definitions were introduced to study the dynamics of anticipation systems. The necessary notions of the theory of computational complexity were presented. An important tool of studying the dynamics of systems is the map of dynamic modes, which construction requires adaptation of procedures for finding periodic trajectories of such type systems. Procedures of determination of periodic trajectories of dynamical systems with anticipation were proposed and described in detail. Time and spatial complexities of construction of states, trajectories, and these procedures, in general, were obtained successively. Representation of states of the corresponding dynamical systems is substantiated by multisets with the purpose of minimization of time complexity on simulation of systems with anticipation. For further optimization of computational costs, it is necessary to take into account the structure of the phase space of a dynamical system with anticipation combining the proposed procedures.
Precision Control System of Chemical Reactor of Continuous Operation
66-76
Oleksii A.
Stopakevich
Odessa National Polytechnic University,
Odessa
Elena O.
Ulitskaya
Institute of Energy and Computer Control Systems of Odessa National Polytechnic University, Odessa
Operation of the precision automatic control system for a continuous chemical reactor of the synthesis of the vitamin B6 is considered. Flows of concentrated nitric acid and a suspension of pyridone with acetic anhydride enter the reactor. The reaction of pyridone with acid is exothermic, therefore, the reactor is provided with a jacket for cooling the mixture. From the point of view of modeling the chemical reactor for the synthesis of vitamin B6 is a reactor of ideal mixing. The reactor model takes into account the mutual influence of parameters, heat transfer and the kinetics of a chemical reaction. The model of automation equipment takes into account its basic properties. The dynamics of actuators, running-down of the shaft speed are considered, which enables the realization of more accurate control. Considering peculiarities of measuring devices of the control system modeling increases the reliability of transient processes and assessment of the system quality. The kernel of the system is the optimal nonlinear multidimensional controller. The control system enables providing high-precision maintenance of the temperature of the exothermic reaction by taking into account the properties of the equipment. In addition, a higher quality compensation of disturbances is achieved by means of the use of the control approach with separation of entering flows in comparison with a typical control system. The developed system has the property of robustness when changing the load of the installation, providing high quality and safety of the synthesis process of the obtained vitamin. Strict maintenance of the technological mode prevents the occurrence of undesirable reactions resulting in admixtures and violation of the homologous formula of vitamin B6. The considered algorithm can serve as the basis for the development of precision automated process control systems of chemical technological type.