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 Âûïóñê 68
- Bure V., Parilina E. Stochastic models of data transmission in networks with different topologies
The game theoretic models of data transmission in networks with different topologies are presented and discussed in the paper. The nodes of the network in which data packages appear for transmission to the destination nodes are interpreted as the players whose aim is to deliver as many packages as possible. To determine the game a system of payoffs and costs that players receive or pay sending packages is proposed. We model dynamic data transmission as a stochastic game. It is assumed that multi-package data transmission is prohibited and all packages have a unit length. We use both non-cooperative and cooperative approaches to solve the game. In noncooperative approach, the Nash equilibrium is considered as an optimality principle. In cooperative approach, players maximize the summarized expected payoff. The optimal player strategies for each approach are obtained. We make conclusions about necessity of the coordination of the players’ strategies to increase the network throughoutput.
- Podinovski V. Reper functions
After discussing the notion of utility and utility function, we introduce a concept of reper value function. It enumerates all the elements of the finite ordered set so that for those elements, which can play the role of reference levels (of preference, quality, efficiency, or, conversely, harm, danger, etc.) and to be characterized by meaningful estimates (e.g., verbal assessments "excellent", "good", etc.) the appropriate numerical scores (e.g., 5, 4, etc.) will be assigned. We give several examples of such functions representing practical interest. They are associated with leximin and leximax relations that are used for modeling of preferences in multicriteria problems with criteria of equal importance, when the decrease in the low values of some criteria are not compensated by an increase in the larger values of other criteria. We show how to build the reference functions when the criteria have different importance, and also when criterial structure is hierarchical.
- Bykov A., Shcherbakov P. Numerical study on effectiveness of surrogates for the matrix l0-quasinorm applied to sparse feedback design
Optimal control problem formulations sometimes require the resulting controller to be sparse, i.e. to contain zero elements in gain matrix. On the one hand, sparse feedback leads to the performance drop if compared with the optimal control, on the other hand, it confers useful properties to the system. For instance, sparse controllers allow to design distributed systems with decentralized feedback. Some sparse formulations require gain matrix of the controller to have special sparse structure, which is characterized by the occurence of zero rows in a matrix. In this paper various approximations to the number of nonzero rows of a matrix are considered to be applied to sparse feedback design in optimal control problems for linear systems. Along with a popular approach based on using the matrix l1-norm, more complex nonconvex surrogates are involved, those surrogates being minimized via special numerical procedures. Effectiveness of the approximations is compared via numerical experiment.
- Avdeeva Z., Kovriga S. On the statement of control problems of the situation with many active stakeholders with use of cognitive maps
The paper proposes the statement of control problems of the situation with many active stakeholders and the general scheme of their solution with use of cognitive maps. This formulation of the problem is suitable for analyzing the problem situation in the conditions of a lack of specific data on the management resources of the ACC and predetermines further specification of the problem under various assumptions about possible resource limitations of the stakeholders in the situation of S. From the point of view of practice, the proposed approach makes it possible to diagnose and predict problem situations caused by a conflict of interests at the stage of strategic monitoring and provide a correction for the development strategy of the socio-economic system (SES).
- Belov M., Novikov D. Models of adaptation in dynamic contracts under stochastic uncertainty
This work synthesizes the ideas of organization systems control theory and contract theory in the case of stochastic uncertainty repeated in time. Results on optimal reward systems for different problems are systematized. New sufficient conditions are given for the optimality of lump-sum and compensative contracts under stochastic uncertainty. Dynamic models of principal’s and agents’ adaptation to the changes in the statistical characteristics of the environment are considered. A classification of dynamic (in a sense of decision taking process) models of reward is given. Contracts between shortsighted center and agents functioning under stochastic uncertainty are considered. Reaction to such uncertainity is, indeed, one of the most crucial functions of control organs, providing adaptivity of their subordinate structural elements. Perspective future venues of research are different methods of describing uncertainity influence on agents, studiyng conditions of contract modification between farsighted center and agents and “dissonance” analysis on complex multielement dynamic organization systems.
- Romanov B. About use of “input-output” model for interconnected enterprises
In this article, possibilities of use of the "input-output" V. Leontief' model for the description of interaction of group of the enterprises are analyzed. The analysis shows that direct application of this model is impossible in view of practical impossibility of realization in V. Leontief's model of the multiproduct approach. Generalization of this model that implements the multiproduct approach is offered. This generalization is performed in such way as to represent the real enterprise as a set of abstract enterprises, each producing only one kind of one product. This set of abstract enterprises, outputting the number of products equal to the number of the abstract enterprises, models the real enterprise outputting the same quantity of products. This generalized model is used as a core of optimization and imitation models, designed to research investment in industrial projects, carried out by groups of enterprises. An example of computing maximum output of producing 4 models of automobiles is given.
- Belov R., Ogorodnikov K. Implementation of modified recurrent-search estimation algorithm of correlation-extremal terrain-aided navigation system
The article discusses the recurrent-search algorithm of correlation-extremal terrain-aided navigation system that is able to estimate horizontal coordinates, altitude and vertical velocity from measurements of the inertial navigation system, radio altimeter and reference information. However, in the presence of failures in measurements and ill-conditioned reference information, this algorithm cannot provide reliable and accurate correction. In relation to the above, it is proposed to introduce the reliability condition that prevents wrong solution to be given in case of ill-conditioned reference information or presence of large errors in measurements. This allows us to find the solution in the presence of failures, and also to limit the influence of errors in the determination of horizontal velocity. Overall effect of reliability conditions is to solve a large number of ill-conditioned cases, but minimize the probability of wrong correction. In addition, the article examines features of the above-stated algorithm, aimed at improving an overall perfor-mance.
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