Vol 79, No 3 (2018)

Application of the Lyapunov method to the stability analysis and search of the 2Dsystem norms gives rise to the algebraic problems interpretable as expansion of the nontrivial matrix polynomials into the sum of squares or as parameterized linear matrix inequalities to be satisfied for certain ranges of the parameter values. The paper demonstrated a mechanism for transformation of such problems arising seeking the H∞-norm and a method for calculation of the H₂-norm of the 2D-systems. Both computational schemes are simpler than the existing results. Numerical examples are presented.

We propose methods to synthesize observers for the state and unknown input influences that ensure that estimation error is finite time bounded with respect to given sets of initial states and admissible trajectories or suppress initial deviations and uncertain bounded in L∞-norm external disturbances for time-varying continuous Lipschitz systems. Here gain coefficients of the observers depend on time and are determined based on numerical solutions of optimization problems with differential linear matrix inequalities or numerical solutions of the corresponding matrix comparison system. With the example of an electric drive system with elastic transmission of motion we show that their application for state estimation and unknown inputs for time-invariant systems proves to be more efficient (with respect to convergence time and accuracy of the resulting estimates) compared to observers with constant coefficients obtained based on numerical solutions of optimization problems with linear matrix inequalities.

Proposed was a mathematical optimization model of the power supply system of a railway segment where the electric power is bought from more than one supplier with allowance for the random demand. Consideration was given to several time periods with different tariffs for electric power. The system model represents a two-step problem of stochastic programming with a quantile criterion. At its first step, a primary purchase plan is generated. At the second step, an additional purchase is done to compensate for the lack of electric power arising because of the random demand. The model takes into consideration the losses arising at transmitting the electric power from the supplier to the segment, as well as the pent-up demand. The total operational costs of the power supply system under consideration are minimized. An algorithm was proposed to solve the problem by reducing the stated problem by discretizing the probabilistic measure and confidence method to the problem of mixed integer linear programming. A model example was discussed.

The developed approach to the fragment method of restoring the operation of digital systems (DS) structured as a minimal quasicomplete graph with two paths between two users is to alternately restore individual DS fragments. The analyzed DS fragment consists of a tested user, a switch, and two communication lines between the switch and the testing and tested users. For a single fragment, we construct a typical base program unit which can serve as a reference for the base units for other DS fragments. Based on the results of diagnostics for the components of the fragment, the testing user replaces functions of the faulty component with functions of operational components. The developed approach guarantees to remove the influence of a single faulty component in a digital system of the analyzed structure.

We consider the problem of constructing approximate Stackelberg solutions in a linear non-zero-sum positional differential game of two players with terminal payoffs and player controls chosen on convex polyhedra. A formalization of player strategies and motions generated by them is based on the formalization and results of the theory of zero-sum positional differential games developed by N.N. Krasovskii and his scientific school. The problem of finding a Stackelberg solution reduces to solving nonstandard optimal control problems. We propose an approach based on operations with convex polyhedra.

The paper is concerned with scheduling the two-way traffic between two stations connected by a single-track railway with a siding. It is shown that if, for each station, the order in which trains leave this station is known or can be found, then for various objective functions an optimal schedule can be constructed in polynomial time using the method of dynamic programming. Based on this result, the paper also presents a polynomial-time algorithm minimising the weighted number of late trains.

This paper presents the single-axis angular motion equations of a large space structure assembled in orbit from separate elastic construction elements. We introduce a method to calculate the parameters of discretely varying dynamical properties of an assembled structure whose model has variable coefficients and inherent attributes of an elastic multi-frequency vibrating system. In addition, we suggest a parametrically tuneable algorithm for powered gyro control of such objects that guarantees desired dynamics at all steps of robotized assembly. Simulation results demonstrate the efficiency of the suggested algorithm.

This paper considers an extension of the actional model of influence in online social networks. Within the framework of this model, the influence and influence levels of separate agents (users) and meta-agents (subsets of users) are calculated on the basis of their actions taking into account the goals of a control subject (a Principal). We study some properties of the influence function. An example illustrates how the actional model can be used to calculate the influence levels of users in a concrete social network under available initial data.

The paper suggests a system area network of supercomputers with an increased number of nodes and different paths between them, which is called a generalized extended multiring. We compare the characteristics of the suggested network and Flattened Butterfly network with the same dimensions of network nodes and diameters.