Applied Mathematics and Control Sciences

A two-stage (stepwise) optimal control problem for linear two-parameter systems with distributed control functions is considered. The aim of the work is to establish the necessary optimality condition under the assumption that the convexity of the set of admissible controls is satisfied and the connection condition is nonlinear. Using increments of the quality functional in the form of two-dimensional linear inhomogeneous systems of difference equations, a formula is obtained that allows one to obtain both a discrete analogue of the Pontryagin maximum principle and to study the case of its degeneration. A theorem is formulated that is an analogue of the discrete Pontryagin maximum principle for the problem under consideration. In the case of special controls, the discrete maximum principle degenerates and, therefore, becomes ineffective, including in the verification sense. Therefore, it is necessary to have new necessary conditions for optimality. A special, in the sense of the Pontryagin maximum principle, case of a discrete maximum condition, under which admissible controls are considered special, is studied. A necessary condition for optimality of singular controls is established.

The problem of heat load optimal regulation in a boiler house considered to provide heat carrier to end users, taking into account the permissible temperature deviations according to the temperature schedule, is relevant for a heat supplying organization. Regulation in a boiler house that feeds a heating network with unknown thermophysical characteristics is a problem that belongs to the class of poorly formalized problems. This is due, not least, to the specific features of heating system exploitation. The problem relatively easily solved at different ambient temperatures and at different times in the data completeness case on the above specific features. Unfortunately, collecting such information is almost impossible. We have to pose and solve the problem under conditions of uncertainty. Therefore, decided to develop an urban heating system virtual stand under data incomplete conditions, which will allow creating a heating system models with various conditions of heat loss, with heat consumers of different categories and different heat energy consumption. It will allow to simulate a changes made without making factual changes in an urban heating system structure. The object of the study is a closed urban heating system with a complex topology, and the subject is calculation models of a heating system, which allow determining the temperature loss of the coolant in the sections of the heating system based on data processing from general house metering devices (GHMD). The aim of the work is to improve the efficiency of an urban heating system management based on data obtained using a virtual stand. A conceptual model developed and the main functionality of the virtual stand implemented. Based on a number of numerical experiments carried out, an algorithm formulated and implemented within the framework of a virtual stand, which makes it possible to determine total thermal resistances values at each section of the heating system from GHMD data. The stand tested on the urban heating system of the Lysva city. The deviation of the temperature values calculated within the framework of the model implemented in the virtual stand from the temperatures obtained from the GHMD did not exceed 5 %. Consequently, this virtual stand can used for more efficient urban heating system management, taking into account the calculation error.

Distributed fiber-optic sensors are becoming an increasingly common solution for monitoring and diagnosing extended information transmission lines, industrial devices, buildings and devices. One of the directions - Brillouin reflectometry, which allows diagnosing a fiber line for changes in ambient temperature or mechanical deformation, is becoming increasingly popular for engineers and researchers. However, modern standards impose increasingly strict requirements on diagnostic systems in terms of the accuracy of determined parameters. For Brillouin reflectometry, where the value of the environmental parameters is determined by the position of the maximum of the Brillouin gain spectrum, the task of more accurately determining this maximum becomes the main one. The paper considers modern computer-computational methods for detecting the maximum of the Brillouin gain spectrum in an optical fiber. The authors note that imperfections in the shape of the optical spectrum, such as the signal-to-noise ratio, as well as possible digital defects that occur during digitization, can significantly impair the accuracy of the system. The authors consider three approaches to detecting the maximum of the spectrum: the classical method of Lorentz curve fitting, the method of cross-correlation with the ideal Lorentzian function, as well as the method of inverse correlation developed by the authors earlier. To combine the results of the work of the three methods, a neural network model was developed that accepts the input data of each method, together with the parameters of noise and distortion of the spectrum. The model is presented in the form of a four-layer perceptron with two hidden layers. As a result, the authors achieved an increase in the accuracy of determining the position of the maximum of the spectrum by 10% on the model data.

The article provides a review of existing project management models and methods using particular game theory tools. The purpose of the review is to determine the current level of the research in this scientific topic, and to determine the most applicable classes of game-theoretic models and methods for the study of particular strategic interactions types that arise at certain stages of the project life cycle. Scientific papers published in international peer-reviewed journals and conferences proceedings over the past 10 years are used as an information base for analytical research. The first part of the article is devoted to the description of the most successful examples of the game-theoretic models’ application for the study of strategic interactions within project management processes. Based on this part, a conclusion is made about the locality of the game theory tools application for solving project management problems, as well as the expediency of developing an integrated approach that allows describing strategic interactions in project management processes in an invariant form. The second part of the article is devoted to the definition of criteria for the existing game-theoretic models’ classification. The classification criteria selected in this part of the article are used later in the third and fourth parts. The third part of the article is devoted to the classification of existing models by the composition of agents participating in the strategic interaction. According to this criterion, the models and methods are divided into the classes "Public-private partnership", "Contractor - contractor", "Contractor - subcontractor", "Subcontractor - subcontractor", "Interactions within the team", "Others". Based on the results of this classification, a conclusion is made about the dominant attention of researchers to the problems of organizing contractual relations and a clear lack of attention to non-contractual relations of performers within the project team. The fourth part of the article is devoted to the classification of existing models by their type. In this classification method, game-theoretic models are divided in two changes: strategic interactions are divided into simultaneous and sequential, as well as cooperative and non-cooperative (within the last class, into zero-sum games and non-zero-sum games). Based on the results of this classification, certain classes of game-theoretic models are determined that are most applicable in the study of strategic interactions in project management processes. The results of the work confirm the prospects of developing both particular game-theoretic models for describing specific strategic interactions that arise during the project implementation, and an invariant approach for describing a project as a complex of the stakeholders’ strategic interactions. The results of the work can be used by researchers to substantiate the relevance of their own research on this topic.