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 Выпуск 92
- Agasandyan G. Minimum yield principle and CC-VaR under partial market forecast
The work continues author’s investigations connected with applying continuous VaR-criterion (CC-VaR) in option markets. A situation, when the investor’s forecast about future probabilistic properties of an underlier is restricted by a partial view, is considered. The incompleteness of investor’s forecast is modeled by introducing into forecast some parameters whose values are chosen by investor market properties considered. A minimum yield principle (MYP) that suggests minimizing the investment yield by the choice of parameters’ values is postulated. By that the investor acquires some security for possible forecast mistakes. The theoretical properties of the principle introduced that has self-sufficient interest and simplifies the analysis in a variety of cases are investigated. Demonstration of the principle is realized analytically by two-sided exponential and uniform distributions and by numerical methods with beta-distributions. The results reassert the adequacy of the principle and of the computation algorithms.
- Mukhin A. Synthesis of static output controllers based on the solving of linear matrix inequalities
One of the most practically demanded methods of control in linear systems is control in the form of a static controller. To implement this control method, it is not necessary to measure all the phase variables of the system. With this method of control, the dimension of the closed system coincides with the dimension of the original object. The problem of static controller synthesis, in general, is reduced to the search for two mutually inverse matrices that satisfy a system of linear matrix inequalities. Such a problem is nonconvex and therefore cannot be solved using the apparatus of linear matrix inequalities. The solution of such a problem is reduced to finding two mutually inverse matrices that satisfy a system of linear matrix inequalities. The article considers a special case of the problem of synthesis of static controllers, which can be reduced to solving a system of linear matrix inequalities. The conditions for the implementation of such a case are shown. Two problems of the synthesis of static controllers are considered: the synthesis of the stabilizing controller and the synthesis of the optimal controller. The obtained results are applied to the stabilization of the electromagnetic suspension when the measured variable is the vertical displacement of the rotor. Graphs of transients are presented. A comparative analysis of the quality of transients in a closed system with calculated static controllers is performed.
- Myachin A., Prokofiev V., Stepanov A. The study of energy sustainability of regions of Russian Federation based on pattern analysis
The study is devoted to the application of ordinal-fixed and ordinal-invariant pattern clustering to study the structure of the energy sector in regions of Russian Federation over a five-year period. Methods for pattern analysis in the work are due to the independence of the final results from the difference in the absolute values ??of indicators and the possibility of combining regions that are similar in structure (based on the indicators under consideration). The choice of ordinal-invariant pattern clustering is due to both the endogenous determination of not only the composition of each pattern, but their number, and the lack of the need to choose the initial sequence of the studied indicators, to which some methods of pattern analysis are sensitive. The study was carried out on the basis of such indicators as: a decrease in the level of electricity losses in the networks, the electric power supply of workers, the volume of electricity produced, specific fuel consumption, the cost of services for technological connection, as well as the number of actual connections. As a result of the study, the features of the energy development of individual subjects were studied. The development patterns were obtained, reflecting the similarity of the internal data structure. Dynamic trajectories of development have been built and groups of subjects have been identified that adhere to a constant strategy from year to year. The above results can be taken into account in the development of state policy in the field of energy efficiency.
- Vykhovanets V. The notional analisys and notional modelling
The article describes notional models that are based on primary mental abstractions: identification, generalization and association. In the process of the notional analysis, a notional model is constructed, which consists of a notional structure and contents of its notions. The notional structure defines each notion as the result of generalization or association of the other notions. The content of the notion is described by enumerable and solvable set consisting of subject domain entities. The main difference between the notional model and the other knowledge models is the refusal to describe the association of the notions in the form of a relationship. In the notional model, the association are the same notion as the generalization, which makes it possible to form the other notions from the associations. All this makes the notional model semantically invariant, i.e. independent in its interpretation from the knowledge of the subject domain. Another difference between notional and conceptual models is the multi-aspect expression of the notions. In order to prove the proposed approach to the representation and processing of knowledge, a formal theory of notions is given. The semantic part of the theory (notional language) proves the methodology of the notional analysis, and its syntactic part (notional calculus) proves the technology of notional modeling. It is proved that the notional language is decidable, complete and consistent, while the notional calculus is decidable and consistent on countable models, but complete only on finite models. The use of the notional analysis improves the expressiveness and clarity of knowledge representation, and the use of the notional models increases the efficiency and reliability of knowledge processing.
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