
Main / Aleksandr Kupriianovich Ivanov
Author: "Aleksandr Kupriianovich Ivanov"
Aleksandr Kupriianovich Ivanov, Doctor of Sciences in Engineering; graduated from the Faculty of Physics at Irkutsk State University, completed his postgraduate studies at Bauman Moscow Technical School, doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist of FRPC JSC ‘RPA ‘Mars’; an author of monographs, tutorial, articles in the field of the mathematical modeling of hierarchical realtime computeraided control systems. email: mars@mv.ruA.K. Ivanov,
Aleksandr Leonidovich Savkin, Candidate of Military Sciences, Associate Professor; graduated from the Ulyanovsk Higher Military Command School of Communications and the Marshal Budjonny Military Academy of Signal Corps; completed his postgraduate studies in the Military Academy of Communications; Head of Science and Engineering Support Department of FRPC JSC ‘RPA ‘Mars’; an author of scientific works, manuals, and articles in the field of the development and modeling of communication control systems, automated information systems. email: mars@mv.ruA.L. Savkin,
Dmitrii Mikhailovich Iastrebov, graduated from the Faculty of Economics and Mathematics of Ulyanovsk State Technical University; Deputy Director General and Head of Complex Research and Development Department of FRPC JSC ‘RPA ‘Mars’; research interests are in the field of computeraided design systems and mathematical modeling. email: mars@mv.ruD.M. Iastrebov,
Sergei Sergeevich Shumilov, graduated from the Radioengineering Faclty of Ulyanovsk State Technical University; Chief Designer of FRPC JSC ‘RPA ‘Mars’; research interests are in the field of computeraided design systems and mathematical modeling. email: mars@mv.ruS.S. Shumilov 

Decisionmaking based on the receptorligand interaction methods
The article deals with the mathematical models of decisionmaking in the management organization systems. The models are based on the receptorligand interaction methods studied in the biokinetics. The article describes an interaction between initial data coming to the organization system and knowledge database generated on the basis of operation experience. The combination of matching pairs creates decisions for resolving problems and achieving the goals. The interaction may take one or more stages. For one stage the models were developed in the form of differential equations when the starting amount of data is not equal to the one in knowledge database. When the amounts are equal, the model is represented as Riccati equation in a special form solving by an indefinite coefficient. The article considers cases when information recourses of initial data and the ones of knowledge database are not uniquely defined. The similar models are developed for two stages of interaction. The article gives the examples of calculation of information recourses amount for a decision in case of different ratios of initial data/ knowledge database.
Organization systems, decisionmaking, mathematical models, receptorligand interaction.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling. 
Aleksandr Kupriianovich Ivanov, Doctor of Sciences in Engineering; graduated from the Faculty of Physics at Irkutsk State University, completed his postgraduate studies at Bauman Moscow Technical School, doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist of FRPC JSC ‘RPA ‘Mars’; an author of monographs, tutorial, articles in the field of the mathematical modeling of hierarchical realtime computer aided control systems. email: mars@mv.ruA.K. Ivanov
Aleksandr Leonidovich Savkin, Candidate of Military Sciences, Associate Professor; graduated from the Ulyanovsk Higher Military Command School of Communications and the Marshal Budjonny Military Academy of Signal Corps; completed his postgraduate studies in the Military Academy of Communications; Head of Science and Engineering Support Department of FRPC JSC ‘RPA ‘Mars’; an author of scientific works, manuals, and articles in the field of the development and modeling of communication control systems, automated information systems. email: mars@mv.ruA.L.Savkin
Ilya Vasilyevich Chernyshev, Candidate of Military Sciences; graduated from the Novosibirsk Electronic Technical Institute of Communications; completed his postgraduate studies at the Marshal Budjonny Military Academy of Signal Corps; Associate Professor of the Department in Organizing Airport Activity and Information Technologies of Ulyanovsk Civil Aviation Institute; an author of textbooks and articles in the field of computeraided control systems design, information technologies, and mathematical modeling. email: chernyshev@ulstu.ruI.V. Chernyshev 

The mathematical models of information decisions in operations controls
The article proves the relevance of developing decisionsupport systems that ensure an automation of intellectual activity of operation controls officers. It gives a brief review of scientific researches in terms of psychology of behavior, perception and thinking; and shows the viability of mathematical models for decisionmaking based on the analogue ones in other science and technology domains having a corresponding mathematical apparatus. The authors create the scheme of information decisions made by operation controls, which includes several stages of initial data conversion and gradient distribution of information resources in a onedimensional space of structural units. The complex of mathematical models for information decision making for three stages of conversion and for various modes of initial data entry has been developed. The first model describes the gradient distribution of initial data in the form of a partial differential equation, while converting stages are given as an ordinary differential one. The second model includes the gradient distribution of initial data and subsequently converted data in the space of operating controls. It is represented as a partial differential system. The third and fourth models additionally incorporate convective terms of partial differential equations. The article gives the analytical solutions of all models and the estimated structures of information resources allocation.
Decisionmaking, mathematical models, partial differential equations, ordinary differential equations.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksandr Kupriianovich Ivanov, Doctor of Sciences in Engineering; graduated from the Faculty of Physics at Irkutsk State University, completed his postgraduate studies at Bauman Moscow Technical School, doctoral studies at Ulyanovsk State Technical University, Chief Staff Scientist of FRPC JSC ‘RPA ‘Mars’; an author of monographs, tutorial, articles in the field of the mathematical modeling of hierarchical realtime computeraided control systems. email: mars@mv.ruA. K. Ivanov


The model of informational interaction in the generation of decisions by command units
The article describes the process of decision generation performed by the operations staff of a command unit as an interaction of three types of information resources, i.e. raw situation information, incoming to the system of control; information resources of knowledge base of the system; and information resources of the decisionmaker experience. Such interaction encompasses an amount of decision information recourses. The differential model of the secondorder reaction is suggested as a mathematical model of interaction similarly to a chemical reaction, if two types of information resources are considered; and the differential model of the thirdorder reaction, if all types of information resources are considered. The method of undetermined coefficients was used to find the analytical solutions of relation between the reaction rate constant and time, volume of interacting resources, and volume of solution results. An interaction mechanism was developed to provide review of the whole information space and selecting of the most promising combinations comprising the final result. Based on this mechanism two methods of finding a solution were described as follows: a slow one that sorts out all combinations in a sequential order, or a quick creative one based on the intuition of a decisionmaker who performs a part of operations simultaneously.
Command unit, decisionmaking, mathematical model.



Sections: Automated control systems
Subjects: Automated control systems. 
Aleksandr Kupriianovich Ivanov, Doctor of Sciences in Engineering; graduated from the Faculty of Physics at Irkutsk State University, completed his postgraduate studies at Bauman Moscow Technical School, doctoral studies at Ulyanovsk State Technical University, Chief Staff Scientist of FRPC JSC ‘RPA ‘Mars’; an author of monographs, tutorial, articles in the field of the mathematical modeling of hierarchical realtime computer aided control systems. email: mars@mv.ruA.K. Ivanov
Aleksandr Leonidovich Savkin, Candidate of Military Science, Associate Professor; graduated from the Ulyanovsk Higher Military Command School of Communications and the Marshal Budjonny Military Academy of Signal Corps; completed his postgraduate studies in the Military Academy of Communications; Head of Science and Engineering Support Department of FRPC JSC ‘RPA ‘Mars’; an author of scientific works, manuals, and articles in the field of the development and modeling of communication control systems, automated information systems. email: mars@mv.ruA.L. Savkin


The decisionmaking model in management bodies
The decisionmaking modeling is based on the analogy of the intellectual activity of officials in the management bodies with inventor’s work described in terms of the catastrophe theory. The formation of decision is presented by motion in a potential field of cusp geometry. A potential function has two minima. The first minimum corresponds to initial data, the second one is in line with the findings reached. For transition, a potential barrier needs to be overcome through the pursuance of the specified research with knowledge accumulation. The activity of officials is divided in two parts. The first stage is a multistage data transformation using known algorithms, and the second one is a creative process for identifying the decision variables. Analytical solutions for three and four stages are obtained. A model of chain reaction is received in the model of the second part. The analogy with chain reactions is determined on grounds of the suggestion that information resources stimulating the intellectual conclusions with the avalanchelike growth of new knowledge are created during initial data transformation.
management bodies, decision making, mathematical model, catastrophe theory.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksandr Kupriianovich Ivanov, Doctor of Sciences in Engineering; graduated from the Faculty of Physics at Irkutsk State University, from the postgraduate studies at Bauman Moscow Technical School, from the Doctoral Studies at Ulyanovsk State Technical University; Chief Staff Scientist of FRPC JSC ‘RPA ‘Mars’; an author of monographs, text book, articles in the field of the mathematical modeling of hierarchical realtime computer aided control systems. email: mars@mv.ruA.K. Ivanov


Modeling spatial transformation of information resources of management bodies
Differential models for information processes of management bodies are constructed, which take into consideration spatial distribution and data transformation. The various forms of heterogeneous data interaction with a diffusion propagation from a general function up to the LotkaVolterra equation are considered. A procedure for researching models with a linearization at special points is described. Oscillatory conditions and information wave transmission are defined. The case of data generation at each point of management body at a logistic law is reduced to the Fisher equation. Diffusion equations with data generation at an exponential rate as well as diffusion equations with convective data propagation, and diffusion equations that take into consideration the generation and convective propagation are solved by methods of transformation of variables and sinus transformation. The approximate results are presented in graphical form. The developed set of mathematical models is aimed to improve the automation level of management bodies, to identify an optimal organization of officials’ activity. The prospects for formalizing the decisionmaking procedure is demonstrated.
Management bodies, information processes, mathematical modeling, differential equation systems.



Sections: Automated control systems
Subjects: Automated control systems. 
Aleksandr Kupriianovich Ivanov, Doctor of Science in Engineering; graduated from the Faculty of Physics at Irkutsk State University; Postgraduate Study at Bauman Moscow Technical School, Doctoral Study at Ulyanovsk State Technical University; Chief Staff Scientist of FRPC JSC ‘RPA ‘Mars’; an author of monographs, text book, articles in the field of the mathematical modeling of hierarchical realtime computeraided control systems. email: mars@mv.ru.A. Ivanov,
Vsevolod Valentinovich Tipikin, Candidate of Science in Engineering; graduated from Radioengineering Faculty at Ulyanovsk State Technical University; Deputy Chief Designer at FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of informationsystem design processes automation. email: mars@mv.ru.V. Tipikin


Modeling Mutual Influence Of Information Flows
The article deals with a subset of data flows that build an information space for bodies of state authority and administration. A subset of information flows is specified. The flows form an information space of the state government and administration bodies. The main features of the subset are the amount of information flows, the behavior of document quantity change in flows, the nature of the mutual influence of documents of various flows. The amount of information flows is specified according to the problem of control loops building. The behavior of document quantity change is limited by linear, exponential and logistic dependencies. Linear and nonlinear models of mutual influence of information flows are built. The models are based on the analogy of documents with the population, which is used in the modern scientific literature in the broad sense. Linear models are formed by a system of differential equations of the first order with constant coefficients. The total ordering of the solution is given, analytical results are obtained for some options. Nonlinear models are formed by the LotkaVolterra equations for two information flows. The behavior of models near stationary points is specified with a restriction on the number of documents and without limitation. Information space, document flows, logistic model, LotkaVolterra equations.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Science in Engineering; graduated from the Faculty of Physics at Irkutsk State University, completed his postgraduate study at Bauman Moscow Technical School, doctoral study at Ulyanovsk State Technical University; Chief Staff Scientist of FRPC JSC 'RPA 'Mars'; an author of monographs, text book, articles in the field of the mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]I. Egorov,
Vladimir Aleksandrovich Baboshin, St. Petersburg National Guard Forces Command Military Institute, Candidate of Sciences in Engineering, Associate Professor; graduated from Ulyanovsk Higher Military Command College of Communications; Associate Professor at the Department of Informatics and Mathematics of St. Petersburg National Guard Forces Command Military Institute; an author of articles and inventions in the field of the analysis and synthesis of information systems and mathematical modeling. [email: boboberst@mail.ru.]A. Moiseev,


Models for Creating the SpecialPurpose Mathematical Support of ComputerAided Control Systems
Authors provide reasons to a promising outlook for creating a technology for the development of specialpurpose mathematical support of the computeraided control system in order to improve the management based on process automation of contentrelated information processing and decisionmaking support. Different specialpurpose software components as well as their development stages are analyzed. A block diagram of specialpurpose mathematical support creating that includes production volume data at each stage and intensity of its growth and decrease. Linear differential equations build the mathematical models for creating the specialpurpose mathematical support. Analytical decisions have been made, curves demonstrating the production volume change at all stages are provided. For mathematical modelling the processes of specialpurpose mathematical support creating and decisionmaking support, authors use the LotkaVolterra equations that demonstrate the creative behavior of designers’ work. The equations obtained are examined for stability. Authors detect approximate decisions. The models built are designed for optimal source distribution among development stages of all the specialpurpose software types. Specialpurpose mathematical support, design technology, mathematical modelling.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars, Doctor of Science in Engineering; graduated from the Faculty of Physics of Irkutsk State University, completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, a manual and articles in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Construction and Application of an Analytical Approximation of Threedimensional Distribution
The algorithm and software for solving a threedimensional distribution problem in the forming of control loops are developed. Experimental research has been carried out. The dependence of the solution time on the dimension of problem determined by the number of control objects, observation means and environmental objects that form control loops has been obtained. A mathematical model of the control loop formation is constructed with the choice of optimal values of the adjustable parameters of control objects and observation means. A solution algorithm is described generally with the optimal distribution being performed at each step of searching the optimal values of adjustable parameters. A solution algorithm is proposed on the basis of an analytical approximation of the threedimensional distribution, which ensures the practical implementation of highdimensional problems with restrictions on time. An approximation equation for the three dimensional distribution is obtained using an analytical approximation of the twodimensional distribution. The equation was verified with experiments proved that it is possible to use it in highdimensional problems. A mathematical formulation and an algorithm for solving the problem of control loop formation are given based on the mobility of control objects and observation means. Control loop, threedimensional distribution, mathematical model, algorithm for solving, analytical dependence.



Sections: Automated control systems
Subjects: Automated control systems. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Science in Engineering; graduated from the Faculty of Physics of Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov,
Vladimir Aleksandrovich Baboshin, St. Petersburg National Guard Forces Command Military Institute, Candidate of Sciences in Engineering, Associate Professor; graduated from Ulyanovsk Higher Military Command College of Communications; Associate Professor at the Department of Informatics and Mathematics of St. Petersburg National Guard Forces Command Military Institute; an author of articles and inventions in the field of the analysis and synthesis of information systems and mathematical modeling. [email: boboberst@mail.ru]V. Baboshin


Optimal Creation of Control Loops
The creation process of control loops in a hierarchical automated control system is determined by a threedimensional task of optimal distribution of control objects, monitoring software, and environment objects. Different variations of control loops are presented. An algorithm of random searching the optimal distribution of twodimensional task with control objects and environment objects is described. The analytical approximation of algorithm is given. It was obtained by the orthogonal transformation and was implemented while planning the control objects usage with regard to changing their location in space. Based on the algorithm of the twodimensional task distribution, the algorithm of random searching the optimal distribution of threedimensional task for one of the variations when each loop was created by the specified elements that are not included in other loops was developed. Following the results of the undertaken analysis, it was found that task time at high dimensionality could not comply with the dynamic of situation changing. The way of applying the analytical dependence for task time reducing is shown as well as the corresponding algorithm is described. The findings of experimental studies carried out by the use of the developed software are given. The obtained results verify the theory. Control loop, distribution task, mathematical model, solution algorithm, analytical dependence.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Science in Engineering; graduated from the Faculty of Physics of Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Distribution Laws of Stochastic Data Volumes on Hierarchical System Objects
The article determines analytical dependences of information resource volumes on objects of the hierarchical control system from initial data volumes incoming to the system. The article considers the following variants such as control when initial data is executive orders from an object of high level; and situation data acquisition and analyzing when initial data comes from an object of low level. It is assumed output data volume at each level to be proportional to input data volume. The calculation procedures of distribution laws and numerical characteristics of stochastic data volumes of all objects at known distribution laws of initial data and random conversion ratio of input data into output data are specified. A simulation model of the hierarchical system is created which allows to obtain distribution functions and probability density of stochastic data volumes of all objects based on known numerical characteristics of the initial data. The simulation results are presented that demonstrate the principle possibility of obtaining distribution laws and their approximation by the normal law. Hierarchical systems, stochastic variables, distribution law, simulating modeling.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Automated control systems. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘Researchand Production Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘Researchand Production Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Mathematical Models of Hierarchical Systems Information Space
The article deals with the ability of the mathematical physics methods application to the modeling of hierarchical systems information space. The information space is created with the situation information flows from objects of the lowest hierarchy level and the arrangement flows from upper objects. Spatial coordinates reproduce the hierarchical levels and the structural units of objects. A knowledge level at a certain place and in a particular time is selected as overall performance of information space. A twodimensional model of noninteracting information flows is built. The model is created with a set of parabolic equations that reflect the data distribution through the structural units of objects of different hierarchy levels. The application of the partition method for solving problems under homogeneous and nonhomogeneous boundary conditions is described. The examples of information wave distribution in a system at periodic external interferences are provided. The twodimensional model of interacting information flows is represented by partial differential equations with two spatial coordinates. The problemsolving procedure in stationary and nonstationary cases under certain boundary conditions and external interferences is shown. Hierarchical systems, information space, equations in mathematical physics, partition method.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics of Irkutsk State University; finished his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, articles, and manuals in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Mathematical Models for Knowledge Management in Design Organizations
The article considers problems of knowledge management in an organization involved in automated systems design. Knowledge is defined as information used in a productive process. The article shows that the key moment is availability of formalized models and unformalized methods for obtaining design solutions. The author gives examples of knowledge applied in organizations for designing automated management systems with the use of corresponding models. The mathematical models of sequential transformation of data into information, information into knowledge, knowledge into design solutions are developed as LotkaVolterra linear differential equation systems. Situations of data occurrence from external and internal data sources, and deterioration of data, information and knowledge are considered. Analytical solutions for linear systems were obtained, researches of stability with the use of Lyapunov method were held, types of critical points were defined. The main trends of the knowledge management system were specified in order to gain competitive edge of the developing products. Design organization, automated systems, knowledge management, mathematical models.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Automated control systems. 
Aleksandr Kupriianovich Ivanov, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region;
graduated from the Faculty of Physics of Irkutsk State University; finished his postgraduate studies at Bauman Moscow Higher
Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal Researchand
Production Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, articles, and
manuals in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


The Optimization Model for Information Processing in Complex Control Systems
The firstorder differential equation systems describing information processing in complex systems were generated. The analytical solutions for consequent information processing with the random number of stages in cases of situation coverage and control planning in a hierarchical system of any dimension were obtained. With the use of the obtained analytical solutions representing dependencies of each object’s information resources volumes on time and information processing speed, the optimization problems of scarce resources allocation were formulated in order to maximize the information volume in the system over the specified period. The author supposes that the relation between information processing speed and dedicated resources is known from the experience of design and control. The formulated problems are solved by the use of standard algorithms of gradient search. In the general case, the results can be obtained with the use of numerical integration of differential equations. The examples for solving problems of consequent schemes of two and fourstage information processing were made. Such schemes show the ability to increase the system quality by effective applying of differential models and operations research methods. Complex systems, differential equations, operations research, information processes.



Sections: Automated control systems
Subjects: Automated control systems, Operational research. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics of Irkutsk State University; finished his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, articles, and the manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Dynamic Models of Information Processes in Hierarchical Control Systems
The dynamic model of situation coverage and control planning processes was constructed on the basis of unified numeration of the hierarchical control system objects. The differential equation system describing information processes was generated for each object of the system. Analytical solutions were obtained for three lower levels of a hierarchy while situation covering and for three upper levels while control planning. Analytical solutions represent dependencies of information resources volumes on time, information processing speed, and initial data volume. The model constructing is based on the condition of information resources volume conservation in case of any transformations. The real ability of the analytical solution of differential equations for objects of all levels is shown. The results of the information processes calculations in twolevel systems are considered. The constructed models allow to hold investigations of certain properties of a system promptly and without significant costs in different situations. For examples, such models allow to estimate the control cycle time while changing speed of information processing on objects. On the stages of design, the use of models gives an opportunity to formalize and automate the search of optimal project solutions and provides improvement in quality and losses in cost. Hierarchical control systems, information processes, differential models.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling, Information systems. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; finished his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov, Andrei Evgenevich Kukin, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Postgraduate Student at the Department of Telecommunication Technologies and Networks of Ulyanovsk State University; graduated from the Faculty of Information Technologies of Ulyanovsk State University; Software Engineer at FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of software design for computeraided control systems. [email: mars@mv.ru]A. Kukin, Ilia Vasilevich Chernyshev, Ulyanovsk State Technical University, Candidate of Military Sciences; graduated from Novosibirsk Electrotechnical Institute of Communications and Ulyanovsk State Technical University; finished his postgraduate studies at the Marshal Budyonny Military Academy of Communications; Associate Professor of the Economics and Management Department at the Faculty of Economics and Mathematics of Ulyanovsk State Technical University; an author of textbooks and articles in the field of computeraided control systems design and modeling. [email: chernyshev@ulstu.ru]I. Chernyshev


Optimizing System Probabilitytime Characteristics With the Use of the Simulation Model
The currently central problem of increasing efficiency of a realtime hierarchical control system through rational resource allocation and reduction of control document development time was considered. The method of constructing a theoretical dependence of system probabilitytime characteristics (pTcH) on corresponding objects characteristics was described. The algorithm for developing approximate analytical dependencies based on approximation of experimental data obtained through simulation was outlined. In order to optimize pTcH, the task of allocating resources among objects in a hierarchical control system was formally set and solved. The authors show, that the system simulation model can be used as a target function instead of an approximate analytical dependence with the current efficiency of computers. The simulation model includes a lot of experiments. The random values of control document development time were set during each experiment. According to the structure and the algorithm, system characteristics are defined. Application of simulation models enhances the set of complex system design tasks solved with the use of operations research methods Computeraided control system, efficiency, optimal design, simulation model.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling, Information systems, Operational research. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Building and Researching Dynamic Models of Information Processes in Complex Systems
The author researches the following schemes of processing information in complex systems: a sequent one with a different number of objects, a two or threelevel hierarchical scheme used in transferring information resources from the lowest levels to the highest ones, and a two or threelevel hierarchical scheme used in transferring information resources from the highest levels to the lowest ones. For all the schemes considered, the mathematical models in the form of linear differential equations with constant coefficients were built under simple but realistic assumptions as follows: the size of information resources does not change in case of processing; the speed of processing information on objects has a linear dependence on the size of information resources; the range of equation constant coefficients chosen allows to get the analytical solution. The author obtains analytical solutions of the system of differential equations showing the relationship between the size of information resources and the time on every object of the information processing schemes considered. The fundamental possibility of analytical solutions for any number of objects in a sequent scheme and any number of levels in a hierarchical system was shown. Dynamic models, information processing, complex systems, differential equations.



Sections: Automated control systems
Subjects: Automated control systems, Architecture of ship's system, Operational research. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Differential Models of Information Processing in Hierarhical Computeraided Control System Authorities
The analysis of information processing in hierarchical computeraided control system authorities is the foundation on which the differential reporting situation and planning models have been constructed. The model of situation report represents heterogeneous differential equation of degree one with constant coefficients and describes the speed of creating output information resources by processing input data originating from subordinate bodies. The equation is solved by applying the method of indefinite coefficients. The analytical results for one, two, and three information sources have been obtained. The planning model represents inhomogeneous combined differential equations with constant coefficients. The combined equations describe the speed of creating routine documents by authorities for subordinate bodies. The solution can be found by applying the method of variation of fundamental system constants. The analytical results for two subordinate bodies have been obtained. The results of calculating output data amount in situation report depending on time and the amount of input data from two or three subordinate bodies were given. The parameters of the differential equation solution for four subordinate bodies have been calculated. Mathematical modeling, information resources, control systems, differential equations.



Sections: Automated control systems
Subjects: Automated control systems, Architecture of ship's system. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’, Doctor of Engineering, Honored Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’; an author of monographs, articles, and a textbook in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov, Evgenii Serafimovich Kukin, Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’, Candidate of Engineering; Associate Professor; graduated from the Faculty of Physics of Voronezh State University; Deputy Chief Designer, Head of the Department at FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of the development of software for computeraided systems. [email: mars@mv.ru]E. Kukin, Ilya Vasilyevich Chernyshev, Ulyanovsk State Technical University, Candidate of Engineering; graduated from Novosibirsk Electrotechnical Institute of Communications and Ulyanovsk State Technical University (UlSTU); finished his postgraduate studies at the Marshal Budyonny Military Academy of Communications; Associate Professor at the Department of Economics and Management of the Faculty of Economics and Mathematics at Ulyanovsk State Technical University; an author of textbooks and articles in the field of computeraided control systems design and modeling. [email: chernyshev@ulstu.ru]I. Chernyshev


Optimal Planning of Control Object Application
The issue of control objects distribution through environment objects taking into account controlled parameters optimization is considered in the article. In order to find the general solution of the problem, the authors plot the mathematical dependence between the criteria for the distribution and the probability of goal attainment under some influences, control objects dependent on controlled parameters, and environment objects’ condition. Mathematical dependence can be found by approximating experimental data got with the use of randomsearch algorithm. In order to rearrange initial dependencies in simple approximating forms, iterative orthogonal representation was used. The possibility of optimal solution search with the use of distribution algorithm without plotting the mathematical dependence was researched. That is occasioned by increasing performance of hierarchical automated control system computer aids. The use of this algorithm instead of approximate mathematical dependencies allows improving the solution accuracy. Moreover, the authors define the problem dimension that makes impossible to solve it using the algorithm for the control in real time. This dimension demands to use mathematical dependencies. Optimal planning, control systems, scheduling algorithm, analytical dependencies.



Sections: Automated control systems
Subjects: Automated control systems. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’; an author of monographs, articles, and a textbook in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Optimization of Hierarchical Control System Stability
Designing of hierarchical control systems with optimal stability indices in condition of price limitation is considered in the article. The formal description of hierarchical system structure and functioning algorithm was made. The choice of optimal solution comes to the operational research on the basis of analytic dependencies between system stability indices and objects stability ones. In order to plot the analytic dependence, the authors propose to approximate the experimental data got in simulation process. The simulation model was made with the use of MonteCarlo method. The paper proposes approximate formula models including orthogonal transformation reducing given dependencies to simple approximate forms. The possibility of direct application of scarce resources distribution search with the increasing performance of computer aids for the purpose of optimizing stability indices of the system is demonstrated. On the base of simulation, optimizing software has been developed. Also the article presents the calculation results that prove reasonability of direct application of simulation models in systems of special class. Stability, hierarchical computeraided control systems, optimal design, simulation.



Sections: Automated control systems
Subjects: Automated control systems. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; finished his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Automated System of Terror Threats Assessment
The author considers the ability to use expert systems in the automated system of terror threats assessment to analyze signs of preparation to commission of terrorist acts and to evaluate threating level. The list of signs of terrorist acts preparation is submitted. These signs include information about facts of terrorist acts preparation, terrorists’ targets and the time of the attacks. The models of developing the expert system knowledge base are offered. The models include random generation of signs and threat assessments corresponding to them. The threat assessments were determined by experienced experts beforehand. Threat assessment automation under actual conditions is implemented through comparison of current characteristics values and characteristics values in the knowledge base and showing the most appropriate variants to the user. The author shows the algorithm of using the expert work in operational activities to assess the real threats in the current conditions and to expand the experience base and training exercises. Automated system, expert systems, knowledge base, operative research activities, terror threats.



Sections: Automated control systems
Subjects: Automated control systems, Artificial intelligence. 
Aleksandr Kupriyanovich Ivanov, Federal ResearchandProduction Center Open Joint Stock Company ‘Research and Production Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Open Joint Stock Company ‘Research and Production Association ‘Mars’; an author of monographs, articles, and a textbook in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Planning Time Estimation in a Hierarchical Control System
Performances of planning efficiency in a hierarchical control system are established. They include the total time distribution laws of plan development in the system from top hierarchical level to separate objects or their collections at all levels. Analytical dependencies of the laws of distribution of total time of development in the system from the laws of planning time distribution on all objects are obtained in general terms. Solutions for standard distribution with known central tendency and mean square deviations are shown. A simulation model designed to compute the approximate laws of total planning time distribution in the system for various number of objects of all levels is proposed. Experimental results are presented for the system with a set structure and operational efficiency of objects. The plotted analytical and algorithmic dependencies allow to estimate the planning time in the hierarchical control system at the development stage with great precision. Algorithmic dependencies as a simulation model are useful at any laws of planning time distribution on objects. Analytical dependencies are accessible at the distribution laws, which are tolerant to the random values toting. Based on the dependencies obtained, it would be possible to create and solve a formalized design problem with optimization of operational efficiency performances at limits for the system cost. Hierarchical control system, planning time, laws of distribution, analytical dependences, simulation.



Sections: Automated control systems
Subjects: Automated control systems. 
Aleksandr Kupriyanovich Ivanov, FRPC OJSC ‘RPA ‘Mars’, Doctor of Engineering, a honoured worker of science and engineering of the Ulyanovsk region; graduated from the Faculty of Physics at Irkutsk State University, finished his postgraduate studies at Moscow Academy named after N.E. Bauman, and his doctoral studies at Ulyanovsk State Technical University; a chief research officer at FRPC OJSC ‘RPA ‘Mars’; an author of monographs, articles and a manual in the field of mathematical modeling of hierarchical realtime C2 systems. [email: mars@mv.ru]A. Ivanov


Mathematical Models for Situation Coverage in a Hierarchical Control System
Abstract An analytical and a simulation models have been developed to cover the situation in a hierarchical C2 system. The analytical model is consistent of dependencies of laws of distribution of the system characteristics from those of separate objects. Characteristics of a separate object define the random time for data collection and processing from all subordinated objects and the random time when an output document is generated for a superior object with the aggregated information about situation. System characteristics define random time to communicate information about situation to all levels of hierarchy. The simulation model includes generation of random time values for an objectbased data processing as per the known characteristics of these objects, and distribution of data according to the structure and an algorithm of the system performance. A set of trials of the simulation model allows us to determine approximate values for system characteristics. There is an example of system characteristics. The developed models allow us to solve the design problem for an optimal distribution of the restricted resources across objects to define their productivity and to achieve the requested parameters of the system responsiveness. Hierarchical control system, situation coverage, analytical model, simulation model.



Sections: Automated control systems
Subjects: Automated control systems. 

Operational Analysis of Realtime Hierarchic C2 Systems
Differential and algebraic equation systems specifying the states of objects in steadystate and unsteadystate conditions of situation coverage and control were composed for objects of each level of the hierarchic computeraided control system (C2 system). Solutions of the algebraic equation systems were received. A possibility for solution of differential equation systems was shown. The equation systems for the joint execution of the situation coverage and control processes of the objects were estimated. Hierarchic c2 system, waiting theory, information density, processing performance, differential equation system, algebraic equation system.



Sections: System analysis, data management and processing
Subjects: Automated control systems, Information systems. 
Alexander Kuprianovich Ivanov, Federal ResearchandProduction Center Open Joint
Stock Company ResearchandProduction Association Mars, Doctor of Engineering, Honoured master of sciences and engineering of Ulyanovsk
Region; graduated from the Faculty of Physics of Irkutsk State University, graduated from the postgraduate studies
at Moscow Higher technical College named after N.E. Bauman; graduated from higher postdoctorate studies at
Ulyanovsk State Technical University; chief research scientist at Federal ResearchandProduction Center Open Joint
Stock Company ResearchandProduction Association Mars; author of a monographs, study letter, articles in the
field of the mathematical modeling of realtime hierarchical computeraided C2 systems [email: mars@mv.ru]A. Ivanov, Evgeny Serafimovich Kukin, Federal ResearchandProduction Center Open
JointStock Company ResearchandProduction Association Mars, Candidate of Engineering, Associate Professor, graduated from the Faculty of Physics of
Voronezh State University; deputy chief designer, head of department at Federal ResearchandProduction Center Open
JointStock Company ResearchandProduction Association Mars; author of articles in the field of the development
of software for computeraided C2 systems [email: mars@mv.ru]E. Kukin, Anatoly Alexanderovich Kupriyanov, Federal ResearchandProduction Center
Open JointStock Company ResearchandProduction Association Mars, Candidate of Engineering, Associate Professor, graduated from the Faculty of
Radioengineering Ulyanovsk Polytechnic Institute; leading staff scientist at Federal ResearchandProduction Center
Open JointStock Company ResearchandProduction Association Mars; is interested in the field of the methodology
of the creation and building of distributed computer systems; author of a monograph, papers and articles in design
and development of local and corporate networks, computeraided packages, and special and generalpurpose
computeraided control systems [email: aakur1828@rambler.ru]A. Kupriyanov


Analysis of Information Systems Functioning
The article deals with a possibility of application of waiting theory to analyze the functioning of information systems while
processing documents flows of different types. Differential and algebraic equation systems describing system states in
stationary and nonstationary operating conditions are built. A possibility of the approximation of parallel elements by one
element with exponential rule of service time distribution is shown. Information systems, waiting theory, intensity of flow, processing performance, differential equation system, algebraic equation system.



Sections: Software and mathematical support of computers, computer systems and networks
Subjects: Mathematical modeling, Information systems. 
Alexander Kupriyanovich Ivanov, Federal ResearchandProduction Center Open JointStock Company 'ResearchandProduction Association 'Mars', Doctor of Engineering, honoured worker in the science and engineering of Ulyanovsk region; graduated from the Faculty of Physics of Irkutsk State University; finished his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; chief staff scientist at FRPC OJSC RPA Mars; author of monographs, a textbook and articles in the field of mathematical modeling of realtime hierarchical computeraided control systems. Phone: +7 (8422) 262 320. [email: mars@mv.ru]A. Ivanov


Optimal Allocation of Resources in a Hierarchical Control System
The article gives a sequence to build a mathematical model for optimal allocation of resources in hierarchical control systems on basis of an experimental deduction of dependencies between efficiency of control agencies and objects and allocated resources. It also cites flowcharts of a program for the calculation of the dependencies, and examples of the solutions. Planning, hierarchical systems, mathematical models, efficiency.



Sections: Mathematical modeling, calculi of approximations and software systems
Subjects: Mathematical modeling, Automated control systems. 
Aleksandr Kupriianovich Ivanov, FRPC OJSC RPA Mars, Doctor of Engineering, graduated from the Faculty of Physics at the Irkutsk State University, finished his postgraduate studies at the Bauman Moscow Higher Technical School and his doctoral studies at the Ulyanovsk State Technical University; chief staff scientist of FRPC OJSC RPA Mars, Professor of the Chair Computer Engineering of the Ulyanovsk State Technical University; author of monographs, a textbook and articles in the field of mathematical modeling of realtime hierarchical computeraided control systems. Phone: +7 (8422) 262 320. [email: mars@mv.ru]A. Ivanov


Planning Algorithm in Hierarchical Control System
The article deals with an order of optimal distribution of objects of hierarchicalsystem control on basis of formation of mathematicalmodel parameters from the lowest levels to the highest ones. It also cites blockdiagrams of programmes implementing the proposed algorithm and the results of experimental investigations. Planning, hierarchical systems, mathematical models.



Sections: Mathematical modeling, calculi of approximations and software systems
Subjects: Automated control systems. 



Sections: Mathematical modeling, calculi of approximation and software systems
Subjects: Mathematical modeling, Architecture of ship's system. 

Optimal Control Under Probable Threat From Single and Group Objects
The article presents mathematical models for optimal control under probable threat from single and group
objects. The developed software has resulted in samples of task solution for selection of a position in an
area, safe maneuvering and the best path between given points. Data analysis, environment, probable threat, optimal control.



Sections: Theoretical issues of automation of command and control processes
Subjects: Automated control systems, Architecture of ship's system. 

Evaluation of Potential Danger From Single and Group Objects
The article suggests schemes for calculation of different factors of potential danger from single and group
objects for separate points, set of points and whole areas as well as for single and several targets taking
into account their movement and movement of objects. Data analysis, environment, potential danger, optimal control.



Sections: Theoretical issues of automation of command and control processes
Subjects: Automated control systems, Architecture of ship's system. 
