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 Выпуск 105
- Promyslov V., Semenkov K., Jharko E. Evaluation of the intrinsic characteristics of a cyberphysical system by the method of network calculus
The paper analyzes the evaluation of the system's own characteristics, the so-called service curve, set in the form of deterministic constraints linking the input of the system and the minimum flow at the output of the system. The service curve estimation is considered within the framework of the Network Calculus method and mini-maxi plus algebra approaches, which form the mathematical basis of the method. To evaluate the service curve, one previously developed method related to the duality of mini and maxi plus algebra transformations is taken, and a new method based on the connection of two types of mini and maxi service curves is proposed. The methods are considered taking into account their application to real systems and existing limitations on measurement capabilities, in particular the finiteness of the definition of the observed data flows. The analysis of the both methods shows that each of the them gives an acceptable service curve, but they need improvement for the calculated service curve to correspond to the maximum system performance mode.
- Malyshev S. Software implementation of the Lax – Friedrichs numerical method for modeling nonstationary problems of gas dynamics
This article is devoted to the software implementation of the numerical Lax-Friedrichs method for modeling nonstationary problems of gas dynamics. The Soda problem is considered in two dimensions. We postulate it in the following way: there is a closed shock tube with a plate in the middle. The plate separates two gases with different thermodynamic characteristics. At the initial moment of time, it is instantly deleted: gases mix and produce a shock wave. The purpose of the work is to find the thermodynamic characteristics at any time and to program the implementation of calculations using the numerical Lax-Friedrichs method. This task is relevant at the moment due to the lack of clear computational algorithms in the field of gas dynamics. The solution depends on the number of cells in the grid into which the surface is divided. As a result, the calculation and numerical values for different grids are given as well as their comparison with the help of various norms is made.
- Antipov A., Tkacheva O. Robust control of the trolley of a single girder overhead crane under the action of unmatched perturbations and incomplete measurement
We considered the problem of controlling an electromechanical system, which is a single-girder overhead crane trolley (mechanical subsystem) with the reduced dynamics of a DC motor (electrical subsystem). The plant operates under conditions of lack of controls, the action of parametric and external perturbations, and incomplete measurements. In this case, the perturbations acting on the mechanical subsystem are unmatched. For safe transfer of payload in these conditions, a number of solutions have been proposed. A reference trolley trajectory with an integral of the angular coordinate has been formed. The presence of the integral part leads to the damping of payload oscillations. It is shown that this part also makes it possible to suppress unmatched wind perturbations. To track the generated trajectory, a procedure for block synthesis of sigmoid fictitious controls in the mechanical subsystem and true discontinuous control in the electrical subsystem has been developed. Smooth and bounded sigmoid functions provide suppression of unmatched perturbations. These functions are implemented in the actuator and do not lead to its strong wear, which occurs during the formation of discontinuous fictitious controls. For information support of the control law, a dynamic differentiator with a sigmoid corrective action has been developed, which provides an estimate of the speed by measuring the tracking error with any given accuracy. The proposed solution will make it possible to abandon the trolley speed sensor and avoid jumps in evaluation signals. The results of numerical simulation of closed-loop systems with discontinuous and sigmoid fictitious controls are presented. They demonstrated the effectiveness of the developed approach.
- Vytovtov K., Barabanova E., Vishnevsky V., Volkova S., Vytovtov G. Algorithm for constructing a system of Kolmogorov equations for studying the transition regime of two-phase queuing systems with a large number of requests
This work is devoted to the development of the Kolmogorov differential equations system constructing algorithm for a single-line queuing system with a Poisson input and phase service. The case of two phase system and an arbitrary finite number of customers in the system is considered. The new functions that significantly simplify the Kolmogorov differential equations system constructing algorithm and the system infinitesimal matrix are introduced. A comparative analysis of the complexity of previous algorithms and the algorithm presented by the authors is carried out too. The use of this algorithm will allow in the future to obtain analytical and numerical solutions of the main performance characteristics of the M/PH/1/n QS with a large number of applications in the transient operation mode.
- Ninidze D., Ougolnitsky G., Usov A. Management of innovation implementation using various information structures
A two-level management system for the innovation implementation in organizations is studied, taking into account the conditions of their "life-ability". The main task of mathematical modeling of the coordination of private and public interests in innovation implementation models is determining the appropriate strategy for the promotion of innovations. The problem is considered in a hierarchical formulation. There is one top-level management entity (center) and several lower-level entities (agents). The center is responsible for the result of innovation implementation, and agents are directly involved in implementation. The center manages the innovation implementation using various information regulations. Agents promote innovations and they receive funds from the center. At the same time, agents bear personal expenses. Agents have their own private interest, namely, they are engaged in third-party activities, that also bring them income. These activities are not related to the innovation implementation. Algorithms for constructing solutions to Germeyer's games in motivation and compulsion are indicated. Numerical solutions are constructed using the method of qualitatively representative simulation scenarios. Simulation experiments were conducted, the analysis of the results obtained was given.
- Kvyatkovskaya I., Vo Thi Huyen Trang, Tran Quoc Toan Development of a recommendation model to support decision-making when the user chooses products
Recommender systems are used to predict user preferences for a particular product or service, and to recommend suitable products or services to the user. Many of the methods used in data mining, related to classification or the construction of association rules, are used in recommender systems. This article proposes a new recommender model that combines association rules and statistical implication index measures. In the proposed model, support and confidence measures are used to create association rules, and the statistical implication index measure is used to filter the set of rules and rank recommendations. The proposed model and algorithms are used to build a recommendation result based on a known data set.
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