Vorotnikov V., gumenyuk I., pozdniakov p.
Abstract. The article is sacred to the questions of estimation of efficiency of division of networks on clusters with the use of methods of nonlinear chart of compromises. For the estimation of efficiency of method of clusterization of network an objective function, is used that is scalar chart of private criteria. As private criteria it is expedient to use the next parameters of network: reliability of network, fluence of energy and volume of service information. An example of calculation of efficiency of division of networks on clusters is made at the use of three private criteries for network from 10 knots. It is shown that for the estimation of efficiency of division of networks on clusters it is necessary to use nonlinear chart of compromises. They got results are actual at the decision of intricate problems. Keywords: Mobile ad hoc networks, network topology, clusters, reliability of network, fluence of energy, volume of service information, efficiency of division, nonlinear chart of compromises IntroductionThe development of information and communication technologies has led to a widespread use of wireless mobile networks with access to the global information network. Such networks are known as Mobile Ad hoc NETworks (MANET) do not have a permanent structure, are mobile, and have different quality of technical composition (2, 22, 24).Communicating over a MANET networks are regulated by the routing protocols which can be divided into three main groups (6, 14, 17 and 20): proactive routing protocols, reactive routing protocols and hybrid protocols.Hybrid protocols combine methods of proactive and reactive protocols on different hierarchical levels, determining, among route search method, the method of partitioning the network into hierarchical structure or clusters. The disadvantage of hybrid protocols is the comparative complexity of the implementation which is connected with the necessity of clustering (19,(25)(26)(27).The efficiency of network clustering depends on many parameters (8, 14): the number of nodes, the distance between nodes (19), the probability of failure-free work of communication channels between nodes (4, 5), the energy efficiency of information exchange between nodes (11, 16), connectedness (reliability) of network (7, 23) and others. Estimation of the efficiency of the method of network clustering is multicriteria problem (1, 3, 13, 15 and 23). Difficulties of criteria choice, that allow building an adequate objective function, are faced in solving this class of problems (27). The problem of constructing an objective function is that the criteria that characterize the network parameters have their limitations.Currently, there are many methods for solving multiobjective problems, which are based on different principles of heuristic regularization or extending the definition of formulation the problem [19, 21 and 26).Another method of solving multiobjective problems is connected with the regularization of incorrect task and reducing it to a task that has only solution (25-27). Such metho...
The paper studies a problem of guaranteed transfer within a finite amount of time of a nonlinear dynamical system subjected to uncontrolled disturbances to a state where a given part of the variables equals zero. The bounded controls are offered to be generated by means of a feedback in form of nonlinear functions of phase variables of a given nonlinear controlled system of differential equations. The method of exact feedback linearization of the nonlinear system is used. As a result, the solution of the original nonlinear problem is narrowed down to solve the linear game-theoretic antagonistic control problem. Sufficient conditions are obtained with ensure that the problem has a guaranteed solution for the given domain of initial conditions. As an example, problem of the space turn of an asymmetric rigid bode (spacecraft) is considered within the framework of the method. Three reaction wheels are employed to produce necessary torque in the axes of the spacecraft. External uncontrolled disturbances, that have no statistical description, are taken into consideration in the process of reorientation. In this case the initial nonlinear controlled systems consists of dynamic Euler equations and Rodriges – Hamilton kinematic equations based on the quaternion parameterization of attitude kinematics. Two problems of the space turn of the spacecraft are considered. 1) The rest - to - rest reorientation problem. 2) The space turn from a stationary state to a given angular position; it is not assumed that the turn takes the spacecraft to a stationary state. The proposed approach allows common positions to give some already well-known solutions of these problems. A new solution of the reorientation problem is also given. For this new solution an estimation of the admissible domain of uncontrolled disturbances is found. Results of a numerical calculations are considered.
Abstract:The article is devoted to the evaluation of fractal properties of routing data in computer large scale networks. Implemented the study of percolation network topological structures of large dimension and made their transformation into fractal macrostructure. An example of calculating the fractal dimension of the data path for the boundary of the phase transition between the states of network connectivity. The dependence of the fractal dimension of the percolation cluster on the size of the square δ-cover and conductivity value network of large dimension. It is shown that for the value of the fractal dimension of the route 5 1.has a stable dynamics of development and size of clusters are optimized with respect to the current load on the network.
The article is sacred to the questions of design of topology of complex networks with the use of new methods of fractal geometry. A complex network structure is in-process synthesized, through replacement of tops of count by a count-fuse, and also the simplest, including affine transformations. The distinguishing feature of pre-fractal counts is possibility of receipt of numeral descriptions of network, coming from the analysis of properties of his counts-fuses. For the got pre-fractal count properties of fractal and scale invariance are investigational. An example of calculation of fractal dimension of pre-fractal count of complex network is made at the use of square and three-cornered blocks for coverage of network. It is shown that for the effective analysis of properties self-similarity of pre-fractal counts it is necessary to use Vcoverage Dependence of fractal dimension of pre-fractal count is investigational on the linear size of grate εcoverage with the purpose of determining the amount of factors, influencing on the system. They got results are actual at the decision of intricate problems.
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