编号 6 (2022)
Mathematical Problems of Control
Design of Integrated Rating Mechanisms Based on Separating Decomposition
摘要
This paper proposes an approach to reducing significantly the computational complexity of optimization problems in the design of integrated rating mechanisms (IRMs). The background concepts are introduced. The representability of a given discrete function as some IRM is proved. The decomposition procedure for a particular training example on some partition of input parameters is considered, and the following results are established under some restrictive conditions. First, an IRM matrix for a particular example of an input data set can be designed by maximizing a certain polynomial. Second, a set of given examples can be implemented by some IRM matrix. Third, an IRM can be implemented on a training data set in a certain complete binary tree based on the decomposition method. Fourth, some discrete function is implemented through a given complete binary tree if the discrete functions represented by convolution matrices are implemented in each node of this tree. All these results are rigorously formulated and proved. An illustrative example of the decomposition procedure based on a complete binary tree on three leaves is given. We propose a method for finding IRMs that implement a given training set in the space of all possible complete binary trees based on the branch table. In addition, we describe the decomposition procedure according to the branch table for each partition of input parameters. Finally, the advantages of the proposed method are outlined.
Control Sciences. 2022;(6):3-13
3-13
Control in Social and Economic Systems
A Strategic Management Model for Restructuring the Technological Core of an Economy
摘要
This paper considers the multi-sector model of the technological core of an economy, mathematical methods for its analysis, and procedures for calculating an indicative plan to restructure the core. The productivity of this core is proposed as a formalized criterion (indicator) for the effectiveness of structural innovations. The following optimization problem is stated: find a balanced state maximizing productivity by planned changes in the output and price indices. An equivalent transformation method is developed for the model considering the achieved values of the indicators. Several propositions concerning the properties of equilibrium and balanced states are proved. As a result, a multistage procedure is constructed to calculate the trajectory bringing the economic system closer to a balanced state. The multi-sector model is analyzed to compare the uncontrolled and controlled modes of development. The uncontrolled mode simulates the state of a market economy: no centralized management of the economy, sustainability, and relatively low GDP growth rates. The controlled mode involves the strategic planning methodology. As shown below, due to indicative strategic planning, the productivity of Russia’s economy can significantly increase even at the first plan implementation stages. The proposed indicative planning methodology is mathematically justified. Numerical examples of its implementation on real statistical data are given. According to the paper’s results, centralized planning institutions should be established for developing the technological infrastructure of Russia’s economy. Such institutions are of current importance due to the international economic and political situation.
Control Sciences. 2022;(6):14-25
14-25
Fuzzy Volatility Models with Application to the Russian Stock Market
摘要
Volatility modeling and forecasting is a topical problem both in scientific circles and in the practice. This paper develops an approach combining the GARCH model and fuzzy logic. The Takagi–Sugeno fuzzy inference scheme is adopted to fuzzify an original autoregression model (the conditional heteroskedasticity model). As a result, several different local GARCH models can be used in different input data domains with soft switching between them. This approach allows considering such phenomena as volatility clustering and asymmetric volatility (the properties of real financial markets). The proposed algorithm is applied to the historical values of the RTS Index and is compared with the classical GARCH model. As demonstrated below, in several cases, fuzzy models have advantages over traditional ones, namely, higher forecasting accuracy. Thus, the proposed method should be considered among others when modeling the volatility of the Russian financial market instruments: it demonstrates qualities superior to the conventional counterparts.
Control Sciences. 2022;(6):26-34
26-34
Control of Technical Systems and Industrial Processes
Estimating Industrial Process Stability by Whitney's Singularity Theory When Choosing a Sufficient Time-Sampling Frequency of the Control Signal
摘要
In this paper, we estimate the stability of continuous-type automated industrial processes and choose a sufficient time-sampling frequency of the control signal using Whitney’s singularity theory. The proposed stability analysis approach is based on constructing typical bifurcations for the historical data of a technological object under different time-sampling frequencies of its control signal. The singularity equation serves for obtaining the equation of the equilibrium state curves of the system and a sufficient time-sampling frequency of the control signal corresponding to the vertex of the resulting curve. As an illustrative example, the developed method is applied to the control system of the mass balance stripping section in the purification process of a styrene distillation column of the ethylbenzene, styrene, and polystyrene plants. Based on the quantitative analysis results, we construct a bifurcation and determine a sufficient time-sampling frequency of the control signal to ensure system stability.
Control Sciences. 2022;(6):35-41
35-41
Control of Moving Objects and Navigation
Analysis of Stress Exposures on Autonomous Navigation Conditions in Search Correlation-Extreme Navigation Systems
摘要
This paper further develops the concept of an applied geographic information system (AGIS) for modeling search correlation-extreme navigation systems (CENSs), which was presented in [4]. As shown below, the AGIS can be configured to perform computational experiments with computer models of the existing CENSs and those undergoing various development stages without programming in universal languages. Strict reliability requirements for CENSs increase the role of testing their computer models under stress exposures. During stress testing, the negative effects of different exposures on autonomous navigation conditions are assessed in application areas. Such exposures are not considered at the CENS design stage (reference point masking, distortion of terrain objects borders, etc.). The exposures that prevent CENSs from performing their tasks effectively (critical exposures) are described. Stability to critical exposures is a strong motivation for improving all CENS elements: sensors of geophysical fields, onboard algorithms, and CENS preparation procedures for performing particular tasks in application areas. The mathematical model of approximation by generalized step functions [4] is used to analyze critical exposures on CENS operation. Computer simulation models of different shooting systems are considered as the most important sources of initial data on the approximated function. The mathematical model of stress exposures on CENSs that match images by the mutual correlation criterion is developed further.
Control Sciences. 2022;(6):42-58
42-58
Chronicle
15th International Conference on Management of Large-Scale System Development (MlLSD’2022)
摘要
The 15th International Conference on Management of Large-Scale System Development (MLSD’2022) was held on September 26–28, 2022, by Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, with the support of the IEEE Russia Section. MLSD’2022 aimed to cover big data management issues, including big data use in various areas of management, as well as the standardization of methods, models, and tools for big data processing. The main theme of the conference was theoretical foundations for the strategic management of large-scale system development in the context of national security. The MLSD’2022 program included 18 plenary papers and 199 sectional papers of leading experts from 30 cities of Belarus, Kazakhstan, China, the USA, and Russia. Amongst them, 155 papers were selected, extended, and published electronically in IEEE Xplore.
Control Sciences. 2022;(6):59-66
59-66