Vol 78, No 1 (2017)

Consideration was given to the problem of stabilization for one class of systems that are nonlinear and uncontrollable in the first approximation. The stabilization problem was solved by considering the nonlinear approximation. The stabilizing control was obtained by the method of Lyapunov function which was constructed as a quadratic form. To determine matrix of this quadratic form, a singular matrix Lyapunov equation was solved. For the system of nonlinear approximation, the stabilizing control was determined explicitly. It was proved that the resulting control solves the problem of stabilizing the original nonlinear system. An ellipsoidal estimate of the attraction domain of the zero stationary point was given.

We consider two-criteria control or filtering problems for linear systems, where one criterion is the level of suppression for Gaussian white noise with unknown covariance, and another is the level of suppression for a deterministic signal of bounded power. We define a new criterion, the level of suppression for stochastic and deterministic disturbances that act jointly in the general case on different inputs. This criterion is characterized in terms of solutions of Riccati equations or linear matrix inequalities. We establish that for the choice of optimal controller or filter with respect to this criterion relative losses with respect to each of the original criteria compared to Pareto optimal solutions do not exceed the value \(1 - {{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. \kern-\nulldelimiterspace} 2}\) . We extend these results to dual control and filtering problems for systems with one input and two outputs, generalize them to the case of N criteria with loss estimate \(1 - {{\sqrt N } \mathord{\left/ {\vphantom {{\sqrt N } N}} \right. \kern-\nulldelimiterspace} N}\), and also apply them for systems with external and initial disturbances. We show a numerical example.

We consider a strongly NP-hard problem of partitioning a finite sequence of vectors in a Euclidean space into two clusters of given size with the criterion of minimizing the total sum of square distances from cluster elements to their centers. The center of the first cluster is subject to optimization, defined by the mean value of all vectors in this cluster. The center of the second cluster is fixed at the origin. The partition is subject to the following condition: the difference between indices of two subsequent vectors included in the first cluster is bounded from above and below by given constants. We propose an exact pseudopolynomial algorithm for the case of a problem where the dimension of the space is fixed, and components of input vectors are integer-valued.

The paper studies the problem of achieving consensus in multi-agent systems in the case where the dependency digraph Γ has no spanning in-tree. We consider the regularization protocol that amounts to the addition of a dummy agent (hub) uniformly connected to the agents. The presence of such a hub guarantees the achievement of an asymptotic consensus. For the “evaporation” of the dummy agent, the strength of its influences on the other agents vanishes, which leads to the concept of latent consensus. We obtain a closed-form expression for the consensus when the connections of the hub are symmetric; in this case, the impact of the hub upon the consensus remains fixed. On the other hand, if the hub is essentially influenced by the agents, whereas its influence on them tends to zero, then the consensus is expressed by the scalar product of the vector of column means of the Laplacian eigenprojection of Γ and the initial state vector of the system. Another protocol, which assumes the presence of vanishingly weak uniform background links between the agents, leads to the same latent consensus.

It was proposed to use the hardware accelerators for analysis and data processing in the systems of logic control on a chip including the interacting processor system, memory, and configurable logic components. The data processing expected execution of operations over the sets of elements each of which can be activated by software and realized in the hardware in parallel networks admitting, if necessary, pipeline processing. New methods of design and use of the sorting and search networks were proposed, and the results of their theoretical and experimental comparison with the existing networks were presented.

We propose new models for analyzing the reliability of repairable systems with failure aftereffect, when the probability distribution of an element’s time to failure changes only during the time when another element is being repaired. The key idea here is the so-called coupling principle for various probability distributions when the system’s operation conditions or the “residual lifetime preservation condition” change. We show a method for constructing a system of integral equations as a universal tool for modeling the reliability of systems under the assumption that time to failure of each element obeys the Weibull distribution.

For a single stationary bearing, we develop a method for generalized identification of a group of moving emitting targets for which we know a priori the possible endpoints of their routes. The method includes estimating the parameters of polynomial models of motion based on pseudomeasurements, coordinates of the route’s endpoint for every target, and also the time when it reaches that point. We find the applicability conditions for our approach and propose a step by step generalized identification algorithm. We show the results of a numerical experiment.

The article presents a review of one-class support vector machine (1-SVM) used when there is not enough data for abnormal technological object’s behavior detection. Investigated are three procedures of the SVM’s kernel parameter evaluation. Two of them are known in literature as the cross validation method and the maximum dispersion method, and the third one is an author-suggested modification of the maximum dispersion method, minimizing the kernel matrix’s entropy. It is shown that for classification without counting training data set ejections the suggested procedure provides the classification’s quality equal to the first one, and with less value of the kernel parameter.

The structure of a complex of key performance indicators of work of production of technological type is considered. Features of determination of the qualitative indexes of work of production entering a complex and an error of their estimates are analyzed.

This paper suggests a speed boosting technique for system area networks in massive parallel multiprocessor computers by decreasing the diameter and increasing the throughput of a pair of opposite simplex rings (a duplex ring), a couple and quadruple of such rings. The result is achieved through replacing a duplex ring with a pair of minimal switched multidimensional rings with different steps in each ring. The decreased diameter and increased throughput of rings appreciably reduce packet delivery delays in system area networks based on the pairs of such rings.