|
|
 Выпуск 91
- Belov M., Novikov D. Classification of mathematical models of activity
Within the framework of the systemic model of activity, the minimum complete set of measurable factors describing it is proposed: action, result of activity (state of the subject of activity), internal state of the subject of activity, his experience and resources used. A system of classifications of mathematical models of activity, taking into account various combinations of these factors, has been introduced. A general model describing the relationship between them is considered. It is shown that particular cases of the general model are the well-known decision-making models, models of mastering individual and collective experience, as well as models of joint dynamics of behavioral and mental components of activity, which are basic for the theory of management of organizational systems.
- Belov I. Anisotropy-based analysis of linear discrete time varying systems with multiplicative noises
In the 90s of the last century the anisotropy-based control theory was introduced. Its techniques are used in control and filtration problems for linear systems with nonrandom matrices and input random disturbances with unknown statistic characteristics. The concept of anisotropy of random vector as measure of deviation of the vector probabilities distribution law from standard Gauss distribution was introduced in the theory. The paper demonstrates the solutions of anisotropy-based analysis problems for the linear discrete systems with multiplicative noises. The problems of anisotropic norm calculation and formulation of anisotropic norm boundness conditions are considered for such systems on the finite horizon. The anisotropic norm boundness conditions are presented in two forms: the Riccati difference equations and the Riccati inequality. The obtained anisotropy-based analysis results allow to solve control and filtration problems for multiplicative noise systems.
- Burkov V., Burkova I., Shchepkin A. Profitability condition in the Leontief model
We consider a model input-output model of Leontief, in which each industry supplies its products to other industries and, accordingly, purchases products from them. In the case where the profit of the industries and the costs of output are given, the model dual to the model of Leontief allows us to calculate the equilibrium prices. The paper assumes that the price of products and production costs are set by the industries themselves. For the prices set by the industries, the task is to study their impact on the preservation of the interindustry balance. If we assume that industries are monopolists who, taking advantage of their monopoly position, seek to increase their profits by increasing the price of their products, then the problem arises of determining the conditions of profitability, that is, determining such a set of prices for the products of industries in which all industries make a profit. Assuming that the state cannot influence the prices of the monopolist, measures are proposed to influence the monopolists by the state by imposing restrictions on their profitability or by using cost-saving mechanism. The effectiveness of these measures is evaluated. For the proposed measures to influence monopolies, the conditions for maintaining the interindustry balance and the conditions for profitability are determined.
- Akinfiev V. Models of spatial development of infrastructure systems
We present formulation and methods for solving the problem of spatial development production and transport systems (PTS). The problem is being studied in two versions. In the first version, the PTS include a coordinating unit and a set of production units (enterprises) and transport infrastructure that connects production units with regions (markets) of consumption. In this case, the problem of choosing an investment program for the development of PTS is formulated as an optimization problem with continuous and integer variables. In the second version, we assume that the coordination of investment programs for the development of PTS units is carried out using market mechanisms. The problem statement is proposed, which is formulated as a set of interrelated nonlinear optimization problems with coupled variables. To select the strategic behavior of companies, methods are proposed for reducing the original problem to solving the mixed complementarity problem (MCP), as well as methods developed for solving programming problems with equilibrium constraints (MPEC). The prospects and directions of using the proposed methods for solving applied problems of spatial development of infrastructural systems are discussed.
- Pankratov P., Malakhov I. Actual and perspective methods of constructing wireless access networks in underwater acoustic communication
The large delay in the propagation of signals, the strong influence of reflected signals and, as a result, the high probability of error rate and low data transfer speed are distinctive features of underwater acoustic communication networks from packet radio networks. In such circumstances, the construction of a wireless underwater access network requires the development of special media access control protocols, since many advanced network protocols developed for terrestrial radio networks had extremely low data transmission efficiency in an underwater environment. This article provides an overview of available solutions for promising methods of building a wireless access network in underwater acoustic communication, which are schedule-based and competition-based media access protocols. The ALOHA protocol and its modifications (ALOHA-CA and ALOHA-AN), protocols with the carrier determination mechanism (FAMA and Slotted FAMA), the improved MACAW protocol, UW-MAC and Tone Lohi protocols are also described in this article. Deciding on which protocol to use within a deployable network is an important task in network design. The article provides a comparison of protocols and proposes a way of analyzing in which systems these protocols could be applied. At the end of the work, an analysis of possible scenarios for the application of various protocols in the underwater acoustic communication environment and ideas for additional research in medium access control protocols development was provided.
|
|
