ISSN 1991-2927

## Author: "Aleksandr Kupriianovich Ivanov"

 A. Ivanov
 Construction and Application of an Analytical Approximation of Three-dimensional Distribution The algorithm and software for solving a three-dimensional 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 three-dimensional distribution, which ensures the practical implementation of high-dimensional problems with restrictions on time. An approximation equation for the three- dimensional distribution is obtained using an analytical approximation of the two-dimensional distribution. The equation was verified with experiments proved that it is possible to use it in high-dimensional 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, three-dimensional distribution, mathematical model, algorithm for solving, analytical dependence.
 2019_ 1

Sections: Automated control systems

Subjects: Automated control systems.

 A. Ivanov, V. Baboshin
 Optimal Creation of Control Loops The creation process of control loops in a hierarchical automated control system is determined by a three-dimensional 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 two-dimensional 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 two-dimensional task distribution, the algorithm of random searching the optimal distribution of three-dimensional 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.
 2018_ 4

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling.

 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.
 2018_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling, Automated control systems.

 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 two-dimensional 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 two-dimensional model of interacting information flows is represented by partial differential equations with two spatial coordinates. The problem-solving 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.
 2018_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 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 Lotka-Volterra 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.
 2017_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Automated control systems.

 A. Ivanov
 The Optimization Model for Information Processing in Complex Control Systems The first-order 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 four-stage 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.
 2016_ 4

Sections: Automated control systems

Subjects: Automated control systems, Operational research.

 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 two-level 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.
 2016_ 3

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling, Information systems.

 A. Ivanov, A. Kukin, I. Chernyshev
 Optimizing System Probability-time Characteristics With the Use of the Simulation Model The currently central problem of increasing efficiency of a real-time 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 probability-time 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 methodsComputer-aided control system, efficiency, optimal design, simulation model.
 2016_ 3

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling, Information systems, Operational research.

 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 three-level hierarchical scheme used in transferring information resources from the lowest levels to the highest ones, and a two- or three-level 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.
 2016_ 1

Sections: Automated control systems

Subjects: Automated control systems, Architecture of ship's system, Operational research.

 A. Ivanov
 Differential Models of Information Processing in Hierarhical Computer-aided Control System Authorities The analysis of information processing in hierarchical computer-aided 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.
 2015_ 4

Sections: Automated control systems

Subjects: Automated control systems, Architecture of ship's system.

 A. Ivanov, E. Kukin, 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 random-search 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.
 2015_ 3

Sections: Automated control systems

Subjects: Automated control systems.

 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 Monte-Carlo 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 computer-aided control systems, optimal design, simulation.
 2015_ 3

Sections: Automated control systems

Subjects: Automated control systems.

 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.
 2015_ 2

Sections: Automated control systems

Subjects: Automated control systems, Artificial intelligence.

 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 distribu-tion 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 ob-tained, 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.
 2014_ 4

Sections: Automated control systems

Subjects: Automated control systems.

 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 object-based 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.
 2014_ 1

Sections: Automated control systems

Subjects: Automated control systems.

 A. Ivanov
 Operational Analysis of Real-time Hierarchic C2 Systems Differential and algebraic equation systems specifying the states of objects in steady-state and unsteady-state conditions of situation coverage and control were composed for objects of each level of the hierarchic computer-aided 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.
 2013_ 3

Sections: System analysis, data management and processing

Subjects: Automated control systems, Information systems.

 A. Ivanov, E. Kukin, 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.
 2013_ 1

Sections: Software and mathematical support of computers, computer systems and networks

Subjects: Mathematical modeling, Information systems.

 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.
 2011_ 3

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Mathematical modeling, Automated control systems.

 A. Ivanov
 Planning Algorithm in Hierarchical Control System The article deals with an order of optimal distribution of objects of hierarchical-system control on basis of formation of mathematical-model parameters from the lowest levels to the highest ones. It also cites block-diagrams of programmes implementing the proposed algorithm and the results of experimental investigations.Planning, hierarchical systems, mathematical models.
 2011_ 1

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Automated control systems.

 A. Ivanov
 Distribution Laws for Parameters of Probable Danger From Single Objects The article deals with simulation capabilities for search for laws of distribution of parameters of probable danger from single objects having random coordinates. It gives program flowcharts for simulation and study results.Simulation, probable danger, distribution laws.
 2010_ 3

Sections: Mathematical modeling, calculi of approximation and software systems

Subjects: Mathematical modeling, Architecture of ship's system.

 A. Ivanov
 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.
 2010_ 1

Sections: Theoretical issues of automation of command and control processes

Subjects: Automated control systems, Architecture of ship's system.

 A. Ivanov
 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.
 2009_ 4

Sections: Theoretical issues of automation of command and control processes

Subjects: Automated control systems, Architecture of ship's system.

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