Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
52
2
2020
Four-Mode Model of Dynamics of Distributed Systems
1-12
10.1615/JAutomatInfScien.v52.i2.10
Yuriy I.
Kaliukh
State Research Institute of Building
Constructions, Telecommunications and
Global Information Space of National
Academy of Sciences of Ukraine, Kiev
Yaroslav A.
Berchun
Telecommunications and Global Information
Space of National Academy of Sciences of
Ukraine, Kiev
four-mode model
distributed systems
loop
numerical simulation
Distributed systems are widely used in practice. These are cosmic ligaments in the near-Earth space with the length of tens of kilometers. They approximate reinforced concrete piles in a soil when calculating the stress-strain state and assessing the technical conditions; pipelines both in an air and in liquid, underwater towed systems. Known underwater airlift systems of great length for the extraction of minerals (nodules) from the ocean floor with a length of 5-10 km are known. To solve the problems of the dynamics of such systems in various environments the known mathematical models are not quite correct in terms of taking into account the variety of wave processes. This determines the need to build refined wave models. A new quasilinear mathematical model which describes the nonlinear four-mode dynamics of the distributed system in the spatially inhomogeneous fields of mass and surface forces has been obtained. It is described by a nonlinear system of twelve first order partial differential equations. For it the principles of limitation and hyperbolicity are fulfilled. Together with the boundary and initial conditions the model can be used to describe the dynamics and statics of geometrically and physically nonlinear rod elements, piles in the ground, crane equipment ropes, mine lifts, aerial cableways, towed systems in liquid and gas flows, etc. For two-mode spatial reduction of the model the theorem about correctness of Cauchy problem has been considered. The model has been tested based on numerical solution of the spatial problem of the propagation of four waves of three types: longitudinal, configurational in the direction of the normal and binormal and the torsioned ones. The necessary quantitative estimates of the twist angle and the torque for the specific distributed system in the liquid flow were determined using the numerical algorithm and the program based on the finite-difference method.
Optimization of Partitioning the Domain into Subdomains According to Given Limitation of Space
13-26
10.1615/JAutomatInfScien.v52.i2.20
Valentina M.
Komyak
National University of Civil Defense of
Ukraine, Kharkov
Alexander N.
Sobol
National University of Civil Defense of
Ukraine, Kiev
Alexander N.
Danilin
National University of Civil Defense of
Ukraine, Kharkov
Vladimir V.
Komyak
National University of Civil Defense of
Ukraine, Kharkov
Kyazim Takhir ogly
Kyazimov
Academy of Ministry of Emergency
Situations of Azerbaijan, Baku (Azerbaijan)
geometric object
geometric information
partitioning
tracing
configuration space
generalized variables
mathematical model
optimization
The tasks of geometric design (packaging, layout, coating, partitioning) consists in optimizing the display of geometric information about objects in accordance with a given quality criterion and limitations. The geometric information about a geometric object consists of three components: spatial form, metric form parameters that determine their sizes, and spatial placement parameters. The configuration space of geometric objects is based on the formalization of the concept of geometric information. The mapping of many objects onto their configuration space according to a given set of restrictions defines the spatial configuration of geometric objects. The article introduces the concept of the spatial configuration of partitioning a domain into subdomains via which a new model of its partitioning into two types of subdomains is constructed, each of which is divided into subdomains according to different quality criteria and limitations. As an example, the problem of partitioning a three-dimensional domain (building) into two types of subdomains has been solved, the former is the subdomains for the functional purpose (premises) with maximization of their volumes taking into account design standards. The latter is the subdomains that determine a rational network of routes, according to a given criterion, an example of which is the time of complete evacuation of people from a building with constraints on both the flow parameters of the people and the metric characteristics of the routes in view of the design standards. Petri nets are used to calculate the time of movement of homogeneous flows of people, and their sequential individual and flow movement is used for the heterogeneous flows of people. Consideration of metric characteristics and placement parameters of objects as generalized independent variables will allow us to propose new mathematical models and optimization methods for synthesizing spatial configurations in the future and can be used, for example, when partitioning vehicles compartments during cargo transportation and storage in pattern recognition systems, robotics, etc.
Pontryagin First Direct Method for Differential Inclusions
27-41
10.1615/JAutomatInfScien.v52.i2.30
Ikromjon M.
Iskanadjiev
Tashkent Chemical-Technological Institute,
Tashkent (Uzbekistan)
differential games
differential inclusion
strategy
pursuer
evader
pursuit
admissible control
integral
partition
multivalued mapping
approximate formulae
Pontryagin direct methods are of great importance in the development of the theory of differential games and its application to specific applied problems. It turned out to be useful in control theory under conditions of uncertainty, also in solving the problem of control synthesis. Numerous studies deal with the corresponding theory. Direct methods have proved themselves as an effective means for solving problems of pursuit and control. Pontryagin direct methods consider integrals, having a number of significant differences from the classical integral. One of the differences consists in the use of multi-valued mapping. The second difference is connected with the application of the geometric difference (the Minkowski difference) and the intersection of sets in this operation. In this connection, some difficulties arise in these integrals calculation. In this paper, we consider a differential game described by differential inclusions z ∈ −F(t, ν), where F is continuous compactvalued mapping. The first direct method deals with such classes of games. In particular, the class of stroboscopic strategies of the pursuer, the trajectory of the system are determined. For these classes of games, it is proved that if the starting point belongs to the first integral (the integral from the multivalued (compact-valued) mapping, which is present in the definition of the first direct method, then this is the necessary and sufficient condition for completing the game at a fixed point in time in the class of stroboscopic strategies. Schemes for the approximate calculation of the integral of the first direct method are proposed. The approximation properties of this integral are studied and the stability of these integrals with respect to initial data of the differential game is proved. It is shown that the first integral is stable for unilateral perturbations.
Quantitative Analysis of the Problem of Lion and Man in the Presence of a Circular Obstacle
42-52
10.1615/JAutomatInfScien.v52.i2.40
Mashrabjon Sh.
Mamatov
Mirzo Ulugbek National University of
Uzbekistan, Tashkent (Uzbekistan)
Azizkhon Olimkhon ugli
Zunnunov
Mirzo Ulugbek National University of
Uzbekistan, Tashkent (Uzbekistan)
Egamberdi E.
Esonov
Islam Karimov Tashkent State Technical
University, Tashkent (Uzbekistan)
pursuit
evasion
pursuit control
evasion control
pursuer
evader
In this work, it is considered the problem of Lion and Man in the sense of the l-capture, i.e. hit some neighborhood in the presence of a circular obstacle. A structure is proposed for constructing piecewise-constant pursuit controls that ensure the completion of the game in a finite time. A top estimate of the time of the game was obtained to complete the pursuit.
On Some Applications of Isometricity of Functional Spaces in Applied Mathematics
53-62
10.1615/JAutomatInfScien.v52.i2.50
Dmitriy N.
Bushev
Lesya Ukrainka Eastern European National
University, Lutsk
isometric spaces
Kolmogorov width
best approximation
linear operator
delta kernel
Problems of computational mathematics are directly connected with an implementation of mathematical models in conditions of limited initial information. This is especially evident when, during modeling, one encounters various idealizations of real processes which in turn forces one to apply discretization for functions of continuous variables, as well as replacing all infinitesimal and infinitely large quantities with some finite quantities. That is why the search for a mathematical description of the model or the choice between several possible ones is the most difficult and crucial moment in modeling, since the model may contain a sufficiently large number of connections, parts, variables and choosing the wrong mathematical description for any of them can yield a full or partial operability of the model as a whole. To describe the interactions one selects a priory known functional dependencies. One of the most interesting problems of computational mathematics that require a delicate approach to choosing both the space in which the problem is solved and its capability to scale up quickly the results from a small number of parameters to a much larger number of them, are exactly the problems of approach-evasion differential games, the problems of escape or evasion from a meeting, the problems of escape from a group of pursuers. In solving these problems and in applying the results to minimize redundancy of calculations, it is certainly important to select appropriately a functional space with possible inherent isometry properties. The choice of such space is a separate task requiring a deep comprehensive study. The spaces of real functions of n + k variables that are isometric to the spaces of real functions defined on the n-dimensional Euclidean space are already studied in detail. In this paper, isometric mappings are considered of the spaces of real functions of n + m variables into the spaces of real functions of n variables that are 2π-periodic in each variable, which in turn will contribute to the study of complex controlled systems, as well as finding an optimal mathematical models for such systems.
Coordination of Configurations of Complex Organizational and Technical Systems for Development of Agricultural Sector Branches
63-76
10.1615/JAutomatInfScien.v52.i2.60
Anatoliy N.
Tryhuba
Lvov National Agrarian University, Lvov
Bogdan V.
Batyuk
Stepan Gzhitskiy National University of
Veterinary Medicine and Biotechnologies,
Lvov
Mikhail L.
Dyndyn
Stepan Gzhitskiy National University of
Veterinary Medicine and Biotechnologies,
Lvov
coordination
configuration
organizational and technical system
dairy cattle industry
agricultural sector
simulation modeling
The study is devoted to the system coordination of configurations of complex organizational and technical systems (OTS) for the development of agricultural sector branches. It is based on simulation modeling of the components of organizational and technical systems. The scientific and methodological foundations for coordinating the configurations of complex organizational and technical systems have been developed. They provide for the simulation modeling of complex systems at five levels − operations, partial and generalized technological processes, projects and programs. Simulation modeling is carried out taking into account the changing climatic and production conditions for a given administrative territory that ensures an adequate determination of value indicators. Systems coordination of the configuration of the system for the cooperative production of dairy products for the climatic and production conditions of Brodovskiy district of Lvov region was performed. Simulation modeling of a complex organizational and technical system was carried out at two hierarchical levels (fodder and milk production). It was established that the need for technical equipment for milking cows varies discretely and depends both on the productivity of milking machines and the productivity of the dairy herd. It was established that under the given production conditions of the Zabolottsovskoy community of the Brodovsky district of Lvov region, a cooperative should be created with fodder production to provide family dairy farms that will serve 165 heads. The effective configuration of projects for creating fodder and milk production systems has been determined. The obtained regularities of changes in the value indicators of complex OTS by the example of the development of the dairy cattle industry indicate that the developed scientific and methodological foundations have practical application. They can be used in similar or other sectors of the agricultural sector of different countries, taking into account the specific project environment for taking qualitative management decisions regarding their development.