No. 2, 2014
Abstract. The paper considers mathematical models of conformal behavior that have been developing starting with works of Granovetter and Schelling. The modern mathematical models of conformity, which are investigated by methods of probability theory, game theory and statistical physics are considered in details. The possible applications of mathematical models in accordance with the proposed classification are presented.
Keywords: conformal behavior, social interaction, a model of critical mass, the threshold model of social interaction, social-physics model, crowd control.
Analysis and Design of Control Systems
Abstract. The paper considers the existence of steady-states (asymptotically stable) in positive nonlinear normalized models (PNM) and control for such states in positive orthant K of Rn. The graph model of PNM is a functional graph. Using the notion of admissible control (with coordinates in (0, 1]) a convexity of stable states set in PNM generated by admissible controls has been proved. The issues of PNM movement from any initial state in K to some predetermined stable state in K have been solved (in asymptotical sense) for open-loop PNM and for PNM with linear state feedback. The appropriate procedures are illustrated by numerical example.
Keywords: positive nonlinear model, fixed point of power of nonlinear operator, admissible control, open-loop and closed models.
Abstract. Algorithm for numerical construction of time-periodic Luapunov functions that fall in the prescribed parametric classes is built for use in continuous time-varying control systems with periodic constraints imposed on their parameters. This algorithm is based on the solution of appropriate minimax problems in mathematical programming. The convergence of the developed algorithm is established and example of its computer implementation is given.
Keywords: continuous time-varying control systems, periodic constraints, Luapunov functions, algolithm for numerical construction, parametric classes, minimax problem, mathematical programming.
Control in Social and Economic Systems
Abstract. The paper presents one approach to analytical support of sports teams management and professional development paths of individual players based on data pattern analysis and structural pattern recognition. The proposed approach is implemented for football domain.
Keywords: data patterns, data patterns analysis, analytical applications, decision support systems, best practice, PDL, formal grammars, structural pattern recognition.
Abstract. The paper considers one implementation of Schelling racial segregation model. The model formal description and behavior estimation based on correspondence of modeling process and some Markov chain is presented. Proof is built that clearly explains such model behavior. It is shown that methods and statements used in this proof can also be used for other models and systems behavior analysis.
Keywords: multiagent systems, imitation modeling, Schelling segregation model, Markov chains, stationary distribution, log-linear behavioral rule.
Abstract. The paper proposes and studies the dynamic model of applied research efficiency within the frameworks of innovation project taking into account the schedule of research funding.
Keywords: research projects, mathematical modeling, project efficiency, innovation.
Control of Complex Technological Processes and Productions
Abstract. The paper discusses an optimization problem of the backbone electric network of electric power systems. The methodological approach to solving the problem is given. The algorithms for consideration of reliability criteria for the considered problem are presented. The possibilities of using the geoinformation technologies are demonstrated.
Keywords: backbone electric network, electric power system, optimization for electric network expansion, structural model, reliability, software package, geoinformation technology.
Abstract. The model of GLOBUS-M tokamak (Ioffe Institute, St. Petersburg, Russia) without plasma is presented. The passive structures are taken into account in the GLOBUS-M’s tokamak model. The multivariable control system of the currents in the poloidal field coils with regard to control of the poloidal magnetic flux in the vacuum vessel of the tokamak is developed. The results of the system numerical simulation in MATLAB environment are presented.
Keywords: tokamak, multivariable system, tracking, magnetic control, channel decoupling, poloidal flux, Green’s function.
Abstract. The theoretical analysis of the problem of long-term optimization of harvesting of the population migrating in a reservoir is carried out. On the basis of dynamic programming method and theory of monotonous operators the main properties of optimum trade are established. The process of migration is set by a Markov matrix which changes from initial state to some final state under the influence of model processes of adaptation. The regularities of family of final matrixes of migration are discovered on the bases of computer experiments. The key role of the positive own vector of such matrixes which characterizes residence time of population on areas is shown.
Keywords: discrete model, migration matrix, perron’s vector, residence time, Bellman's function.
Moving Objects Control and Navigation
Abstract. Bearings-only multiple targets tracking in clutter is considered. Several suboptimal approaches of Ried’s Multiple Hypothesis Tracking and PHD-filtering are investigated. PHD algorithms include Sequential Monte Carlo and Gaussian mixture approach. Gaussian Mixture PHD is chosen as the best suitable approach for this problem.
Keywords: multiple targets tracking, bearings-only measurements, multiple hypothesis tracking, probability hypothesis density filtering.