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- Novikov D. A. Network models in control: an introduction from the editor-in-chief
- Baturin V. A., Lempert A. A. Improving method for discrete plant with network structure
The paper is devoted to design of approximate methods of the optimal control problem solution for the network-structured discrete plant. The methods developed are based on Krotov sufficient conditions of optimality.
- Blumin S. L. Dihypergraphs: matrix representations
Incidence matrices construction routine is proposed for dihypergraphs. It uses relevant degrees of unity root to describe hyperpoints and hyperarcs orientation. Valence and adjacency matrices along with Laplacians are also constructed for dihypergraphs and their duals.
- Burkov V. N., Burkova I. V. Network programming in project management
The method of network programming was developed to give exact or approximate solutions for multi-extremal (in particular, discrete) optimization problems. The idea of the method is based on reduction of the problem in hand to a superposition of simpler problems. The scheme of reduction is conveniently represented in the form of a network (the, so called, network representation), with nodes being the sub-problems. Simple optimization problems are solved at each node, while the solution at the terminal node of the network delivers the upper (or lower) bound estimate for the initial problem. For the tree-shaped network representation the solution at the terminal node of the network delivers the exact solution of the initial optimization problem. This paper surveys applications of the network programming method to the several problems of project management.
- Orlov A. I. Network models of industrial control systems
Use of various sorts of graphs is considered for modeling managerial processes in industry organizations (in particular, for optimization on graphs, and in expert technologies). Conformities of graphs are considered with the other classes of non-numerical mathematical objects – binary relations, binary matrices, pair-wise comparison results. Our earlier discrepancy of the analysis of pair-wise comparisons is corrected. The role of ljusians is shown in concordance testing of expert opinions and classification of expert estimations. Graph theory is widely used in industry; in particular, it is an important component of mathematical toolkit of controlling and management of high technologies.
- Petrov A. E. Dual network models of large-scale systems
The tensor method of dual networks was developed to calculate changes of processes in large-scale systems caused by changes in the structure of links. Dual networks are constructed as dual graphs, and have an invariant of structural transformations. The dual invariant has fundamental character that turns up in the form of the law of preservation of a stream of energy. The invariant provides methods to calculate chains and network models of large-scale systems of variable structure, including network models of economic systems. This paper describes the method and its applications for simulation of a product flow network and a dual network of cash flows.
- Semenov A. S. Fractal evolutionary architectures
The model of architecture of complex evolutionary systems is considered. The model is based on self-similar fractal graphs described by an algebraic system of fractoid. Possible applications of fractal architectures are discussed.
- Abdulin E. R. Method for hypotheses making and testing about user mental actions in human-computer interaction
The new method is offered for hypotheses making and testing about user mental actions in human-computer control systems. This method is used to create interface design for the control systems taking into consideration their specific character. The method is based on the critical-path method and its methodical and mathematical tools. The linear model of interface is used as input data. The analysis of critical-path chart allows making reasonable corrections to the source model and increasing its accuracy.
- Belykh A. A., Shaydulin R. F., Gureev K. A., Kharitonov V. A., Alekseev A. O. Principle of multi-modeling in models of individual preferences
New capabilities of individual preferences studies are substantiated. Linear and non-linear (matrix) methods of complex evaluation allow decreasing dimensionality of the decision-making problem, and analyzing dynamics of qualitative changes in convolution.
- Kononenko A. F., Shevchenko V. V. On capabilities of constructive logical and graphical representations of operational games
Capabilities are considered of logical and graphical representations usage in analysis of game-theoretic models. Game-theoretic models considered are presented in the form of operational games. The principles are postulated of study of strategic interactions at uncertainty with use of interaction representation in the form of constructive logical systems, and also the principles of graphical tools (networks) use in such study are outlined.
- Kulba V. V., Kononov D. A., Chernov I. V., Roshchin P. E., Shuligina O. A. Scenario-based research of complex systems: analysis of group management methods
Main components of scenario-based research methodology are described: the scenario system, the system of scenario analysis, the system of scenario synthesis, basics of scenario calculus. Verbal and formal definitions of a scenario and of its formation stages are given. Application is considered of complex systems’ scenario-based research methodology to the analysis of effectiveness of group management in the socio-economic system of the Amur region of Russian Federation.
- Web-communicator creation costs sharing problem as a cooperative game
We consider a problem of web-communicator creation costs sharing for a given target set of sites. We offer a cooperative model where agents are site owners which create a communicator site in purpose of reducing the average click count of surfing the sites.
- Kharitonov V. A., Alekseyev A. O. Network mechanisms of multiple-factor risks analysis
We study management mechanisms for multiple-factor risks in problems of justification of the discount rate of investment projects. The mechanisms are based on the network models with matrix convolution of risk-generating parameters.
- Akhmetzyanov A. V., Grebennik O. S. Selection of allowable gas extraction modes for wells of gas fields
The approach is considered for solution of a stationary distribution problem of gas pressures and flows of crude gas in gas-gathering systems. The approach meets cumulative gas production requirements and technological constraints as boundary conditions. Clustered gas-gathering systems, which use internal energy of natural gas itself, represent tree structures of pipe lines. Therefore the solution of the stationary mode selection problem is reduced to the solution of a sequence of one-dimensional nonlinear equations with monotone functions.
- Akhmetzyanov A. V., Salnikov A. M., Spiridonov S. V. Multigrid balance models of unsteady flows in complex gas transportation systems
Multigrid variants are suggested for hierarchical flow distribution models to optimize unsteady conditions of gas transport at various levels of dispatcher control of the Unified Gas Supply System of Russia. The multigrid scheme based on the relaxation scheme by R. P. Fedorenko is used to increase calculative accuracy of multilevel methods for each level of the hierarchy of calculations. Generality of the approach is determined by the ease of construction of a multigrid structure and transition operators that provide high-precision discretization on coarse grids without preliminary smoothing and interpolation inherent in classical multigrid methods. The universal multigrid technique in the finite-volume discretization is suitable for objects described by equations with discontinuous and nonlinear coefficients and right members.
- Bandurin I. I. Structure management for operative service of electric networks
An adaptive approach is suggested to structure management of operative service with the aim of minimization of maintenance costs of the service. The technique is offered of choosing the optimal amount of expenses for automation and remote control devices on power substation. The mathematical model is developed of choosing optimal headcount, skills and disposition of operating staff.
- Gordiychuk T. V., Itskov A. G. Some algorithms of optimization and visualization of traffic flows
The algorithm is given of optimal path search in a weighted graph with variable weights. The formula are derived for two-dimensional cubic splines with defect 1.
- Epifanov S. P., Zorkaltsev V. I., Medvezhonkov D. S. Model of hydraulic circuit with flow regulators
The system is introduced of equations and inequalities describing flow distribution in pipeline circuits with automatic flow regulators installed on certain sections. The system under consideration is shown to be equivalent to optimality conditions of some convex optimization problem. This equivalence allows building existence and uniqueness conditions of the solution of the considered system. The model is illustrated with the example.
- Zorkaltsev V. I., Perzhabinsky S. V. Model of power shortage optimization in electric power system
The model of minimization of power shortage in the electrical power system is considered. The model takes into account nonlinear power loss in power lines, and is intended for analysis of reliability problems in electric power systems. The model is reduced to the convex optimization problem. Interior point algorithm using quadratic approximations of constraints is suggested for model implementation. Comparative results of numerical calculations are presented.
- Kornienko S. A., Ougolnitsky G. A. Quality evaluation in production systems of different structure
The model of the system for product quality control is proposed. The problem is set of search of optimal strategy with respect to the model for production systems of different structure. The optimal strategy is calculated with the aim of dynamic programming for the production system of an arbitrary structure.
- Stecura G. G. Mechanisms of objects interaction in network-structured digital systems
Features of operation control in complex digital data processing and control systems with network structure are considered. Need for fast communications in such systems is reasoned. Some mechanisms developed in Institute of Control Sciences of RAS are reviewed, which accelerate interaction of system objects.
- Farkhadov M. P., Petukhova N. V., Efrosinin D. V., Semenova O. V. Modeling hybrid communication center with self-services and threshold queuing control
We consider a queuing model to estimate and optimize a modern architecture hybrid call center with a self-service facility based on computer speech recognition. This center is presented by a two-node network with threshold control of queuing. One of these nodes describes the self-service servers and the other one describes a group of operators. Both nodes are considered as multilinear queuing systems. When not served by the automated service, the customer goes to the group of operators. We obtain stationary probabilities of the system states and derive performance characteristics
- Abramova N. A. Expert verification in formal cognitive map application. Approaches and practices
To reduce impact of human-induced risk in simulation of situations on the basis of formal cognitive maps the expert approach is suggested to verification of cognitive maps, map-based models of situations and simulation results. The main components of the scientific and methodological support for the technological task of expert verification are considered. An original multidisciplinary model of the cognitive process of expert validation is proposed, combining concepts and ideas of cognitive science with computer metaphor of the system interruptions. The model is designed for the integrated development of theoretical means and tools to support expert verification. Practical capabilities of expert verification of cognitive maps and proposed approaches to its instrumental support are shown on the well-known example of the applied cognitive map and results of its simulation.
- Abramova N. A., Voronina T. A., Porcev R. Yu. Ideas of cognitive graphics to support verification of cognitive maps
Application of ideas of cognitive graphics in information technologies supporting solution of problems based on cognitive maps is reasoned. Two methods are presented based on these ideas. The first one supports reading cognitive maps and promotes understanding of the causal structure of a map. The second one supports valid estimation of causal influences aggregated in nodes of a cognitive map.
- Gorelova G. V., Makarova E. L. Modeling correlation between socio-economical system and higher eduction system problems with cognitive approach
Orientation of the higher education system to the requirements of socio-economical system real sector demands consideration of problems, contradictions, new tendencies and application of cognitive modeling, explaining specificity of its forms, rules, modification and development.
- Kulinich A. A. Cognitive maps verification based on processes explanation
The cognitive maps verification method based on explanation of factors values forecasting processes is considered. The method is suggested of explanations construction for qualitative cognitive maps.
- Agaev R. P., Chebotarev P. Yu. Convergence and stability in consensus and coordination problems (a survey of basic results)
This paper is a survey of the basic results on coordination and consensus seeking in multiagent systems and on the stability of the corresponding algorithms. The first part of the paper is devoted to the consensus problem in the discrete time. The second part deals with more general problems of coordination in which every agent is characterized by 2d parameters in the Euclidean space of dimension d. These parameters are the coordinates and velocity components of the agents. We discuss procedures of determining the trajectories converging to a given course and obeying a prescribed geometric configuration of the agents (the agents are moving in formation). The dynamically adjusted speed of each agent is a function of the current parameters of this agent and its ''neighbors.'' The information links between agents are determined by a communication digraph. To stabilize the system, linear feedback is used. The stability of motion is studied in terms that characterize the connectivity of the communication digraph.
- Ambartsumyan A. A. Network-centric control on Petri nets for structured discrete event system
The paper deals with the methodology of control Petri net synthesis developed for real-time automation systems. The methodology is based on the model called a structured discrete event system (SDES) applied to analysis functionality and consistency. In the paper, SDES structure is defined, the technique of SDES controllability analysis is proposed. Developed are the method (based on SDES model) of Petri net synthesis for process modeling, the technique of process net analysis and the synthetic method of supervisor control net providing, jointly with the process net, the fulfillment of initial specifications.
- Babak L. N., Scherbatyuk A. F. About one algorithm for underwater plume source localization based on multi autonomous underwater vehicles usage
The algorithm of underwater plume source localization based on approximation of plume boundary is considered in the paper. More close decisions from different autonomous underwater vehicles have bigger weights for plume source position estimation. Some modeling results of plume source localization for group of four autonomous underwater vehicles are supplemented.
- Granichina N. O. Multi-agent order scheduling system
The mathematical network-based model of multi-agent order scheduling system is suggested. The model is illustrated by the example of a small taxi company
- Zatuliveter Yu. S., Fischenko E. A. Graph-dynamics systems with network-centric control in mathematically uniform field of computer information
As development of ideas of the graph-dynamics, the problems are discussed of implementation of systems of high structural complexity with network-centric control in a global computer environment. The approach is proposed to formation of mathematically uniform field of computer information in global networks on the basis of the calculus of tree-like structures. The universal formalism to presentation and “seamless” programming of distributed graph-dynamic control systems is offered as a part of the approach. The examples are given of systems with network-centric control that can be qualified as graph-dynamic systems.
- Kalyaev I. A., Kapustjan S. G., Gajduk A. R. Self-organizing distributed control systems of intellectual robot groups constructed on the basis of network model
This article develops the methods of self-organization in distributed technical systems. In particular, principles and operation routines of self-organizing control systems for intellectual robot groups are studied. The approach is illustrated by the model example of moving some body in a surface by the group of intellectual robots. The results of simulation are presented.
- Kuznetsov O. P., Zhilyakova L. Yu. Complete bidirectional networks of arbitrary conductivity
The resource network is a flow model represented by an oriented weighted graph in which any two vertices are either not adjacent or connected by a pair of oppositely directed edges. Vertices can contain unlimited amount of resource. The weights of edges indicate the ability to conduct resource from one vertex to the other. The processes of the dynamic distribution of resources in bidirectional complete networks with arbitrary capacity and their stabilization conditions are considered.
- Petrikevich Ya. I. Linear algorithms for control of geometrical allocation of agents in multi-agent systems
Simple and effective linear local algorithms for agents movement and allocation on a line and on a circle are proposed. They are based on the following assumptions: 1) the total number of agents in the system is unknown; 2) the future position of each agent is defined by its own coordinates and coordinates of its closest neighbors; 3) one or both of end agents may be fixed or movable. Stability and convergence for developed systems are proven and a number of examples are given to demonstrate the work of the proposed algorithms.
- Shcherbakov P. S. Formation control: the Van Loan setup and other algorithms
The subject of this note is the algorithm of evolution of a point set on the plane devised in~\cite{vanloan}, which drives the whole system to a certain regular configuration. Generalizations of the algorithm are analyzed, certain new properties are studied, the connection to formation control methods is discussed, and new simpler algorithms of this sort are proposed.
- Baybakova E. Yu. Klochkov V. V. Economic aspects of network organizational structures formation in russian science-intensive industry
The system of economic-mathematical models for economic efficiency and risks of network organizational structures and virtual enterprises formation in science-intensive industry is suggested.
- Gubanov D. A., Novikov D. A. Models of unified informatioon control in homogeneous social networks
Models of unified information control in social networks described by a regular graph of interaction of their members are considered. The main emphasis is on the models taking into account dependence between confidence in information and contents of information.
- Prosvirkin N. Yu. Mathematical economic multi-objective model of interaction in integrated network organization structures
A list of interconnected criteria for interaction of integrated companies is developed. They give quantitative estimates of the costs of physical distribution, delivery period and utilized capacity. A multi-objective optimization model of interactions for integrated companies is developed. Unlimited number of producers and suppliers are supposed in the model. Demand for the production of every supplier is accounted with respect to purchase volumes.
- Raikov A. N. Distributed expert evaluation for decision support
Capabilities of expert-analytic and situation centers, distributed expert assessment routines, methods of implicit (or latent) information disclosure are combined on the basis of methodology of convergent management to provide higher quality of management decision making. Methodology of convergent management provides sufficient structural conditions for convergence of consensus achievement processes in a distributed expert community discussing aims and operative directions. The approach has a number of convincing applications.
- Ratner S. V. Scenarios of stratification in innovation network
Formalization is suggested of the problem of choosing the high-efficiency regime of innovation generation and diffusion processes in a post-industrial society with high level of knowledge networks based on social interactions and extensive and advanced use of modern interactive communication technologies. It is shown that original heterogeneity of knowledge and skills of agents in an innovation network may lead to the gap in educational ties among agents, so stratification of agents occurs by their level of knowledge. Stratification reduces the level of uncertainty when making decisions about innovations in the case then some agents act as mediators responsible for coordination of knowledge diffusion process.
- Ougolnitsky G. A. Simulation and optimization models of complex systems with respect to their structure
It is convenient to simulate matter-energetic processes in complex systems with dynamic directed graphs (digraphs) reflecting the structure of a system. Acyclic digraphs naturally describe the structure of a hierarchical system. Linear programming and optimal control problems based on matrices of these digraphs are considered, examples of their applications are given.
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