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 No. 5, 2014
Mathematical Problems of Control
Sh. Sh. Yusubov On an Optimality of the Singular with Respect to Components Controls in the Goursat – Dourboux Systems (pp. 2-6)
Abstract. The paper proposes the definition of control singular with respect to the part of components in the Pontryagins maximum principle sence and singular with respect to the remain components in the classical sence. New necessary conditions of optimality are derived in the Goursat – Dourboux systems.
Keywords: necessary conditions, optimality, singular with respect to components control.
Analysis and Design of Control Systems
A.G. Alexandrov, D.V. Shatov Frequency-Modal Adaptive Control (pp. 7-13)
Abstract. The method of adaptive control for SISO linear plant in presence of unknown bounded disturbances is proposed. Coefficients of the plant are unknown and can be changed in some particular time points. The adaptation algorithm consists of two procedures: identification and synthesis. The identification procedure is based on the finite-frequency identification of the plant and closed-loop system. The synthesis procedure is based on the modal control technique. The algorithm of modal polynomial selection providing specified accuracy gain and phase margins for the system is proposed. Numerical example of adaptation is provided.
Keywords: adaptive control, identification, modal control.
V.N. Afanasiev, A.A. Semion Controller with Discrete Variable Parameters (pp. 14-19)
Abstract. For a class of nonlinear uncertain dynamic objects presented in the form of models with linear structure and state dependent coefficients the control problem is formulated in the key control differential game with quadratic quality functional. The synthesis of controls which leads to need of Riccati equation solution with parameters depending on states at rate of object functioning is carried out. The method for finding the realizable values of the controller parameters based on the solution of this equation in some points of the trajectory of the system and determining the parameters of the controller to control the corresponding intervals is proposed. The results are illustrated by mathematical modeling of a hypothetical object.
Keywords: nonlinear uncertain dynamic systems, differential games, Hamilton – Jacobi – Isaacs equation, Riccati equation.
S.A. Kochetkov, V.A. Utkin DC Motor Control on The Base of Vortex Algorithm (pp. 20-27)
Abstract. The paper proposes the new control vortex algorithms for a wide class of electromechanical systems based on discontinuous control. The designed vortex algorithms provide full invariance of the closed loop system with respect to unmeasured unmatched disturbances (that do not belong to control space). The simulation results for the direct current drive in the tracking problem show the efficiency of the proposed algorithms.
Keywords: electric drive, direct current drive, asymptotical invariance, external disturbances, relay control algorithm.
Control in Social and Economic Systems
V.V. Breer, D.A. Novikov, A.D. Rogatkin Micro- and Macro-Models of Social Networks. Part 1. Theory Fundamentals (pp. 28-33)
Abstract. The paper considers two approaches to construction and study of social networks models: the macro- and micro-descriptions. In accordance with the first approach the structure of connections in social network is averaged. The behavior of agents is considered in «average». The second approach takes into account the structure of agents influence graph and their individual decision-making. A comparison of these two approaches on the example of the threshold model of collective behavior with one relative threshold is given.
Keywords: random graph, social network, consensus, collective behavior, thresholds.
L.G. Egorova Effectiveness of Different Trading Strategies for Price-Takers (pp. 34-41)
Abstract. Simulation models of stock exchange are developed to explore the dependence between trader’s ability to predict future price change and her wealth and probability of bankruptcy. The paper shows that for the case of cautious behavior (i.e. absence of margin trading) the rate of successful predictions should be just slightly higher than 0,5 and such small value explains why so many people try to trade on the stock exchange.
Keywords: agent-based models, trading strategies, prosperity of an agent, probability of bankruptcy.
E.K. Kornoushenko Multi-Model Approach to Mass Appraisal of Multi-Parameter Plants (pp. 42-49)
Abstract. A new approach to the real estate appraisal is considered. In contrast to traditional approach to mass appraisal that uses a single model for objects assessment, the new approach proposed uses several models. Objects to be estimated are primarily classified and the objects of each class are assessed with use of corresponding model. The new approach significantly increases the credibility of resulting estimates. The practical example is presented.
Keywords: mass appraisal, regression model with continuous (or categorical) dependent variable, classification algorithm, dispersion analysis, Fisher’s linear discriminant analysis.
E.A. Grebenuk, A.V. Malinkina Econometric Analysis of Data for Identification and Dating the Financial Bubbles Timeline (pp. 50-58)
Abstract. The paper considers the new approach to identification and dating timeline of financial bubbles with use of econometric methods of time series analysis. A new approach to identification and dating of bubbles based on detection of change of price and dividend processes types is proposed. The developed algorithm is based on application of sequential analysis.
Keywords: rational bubble, difference-stationary process, the explosive process, Dickey – Fuller unit root test, hypotheses sequential testing algorithm.
Control of Complex Technological Processes and Productions
G.G. Grebenuk, S.M. Nikishov Definition of the Critical Failures Breaking Power Supply of the Set of Objects of a Distribution Electric Network (pp. 59-64)
Abstract. The paper considers the problem of vulnerability of electricity distribution network and finding of critical failures in a given set of power supply network components. A schema for finding of critical network components for accidents assessment and negative effects of the interaction of many technical failures is proposed.
Keywords: vulnerability, assessment of failures, electric networks.
Information Technologies in Control
G.P. Aksenova The Matrix Test Response Analysis Technique for FPGA (pp. 65-69)
Abstract. Test response analysis techniques using a signature analyzer are considered. A new analysis technique that provides a fault location and a low hardware overhead is proposed.
Keywords: application-specific integrated circuit (ASIC), field-programmable gate array, on-line testing, circuit under test, test response analysis, signature analyzer, fault location.
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