Vol 78, No 2 (2017)

We consider a multi-criteria problem of suppressing disturbances with linear feedback with respect to the state or output measured with noise. We assume that the system has N potentially possible inputs for disturbances from given classes, and the criteria are induced norms of operators generated by the system from the corresponding input to the common target output. We obtain necessary Pareto optimality conditions. We show that based on scalar optimization of the suppression level for the disturbances that act on all inputs we can synthesize Pareto suboptimal controllers whose relative losses compared to Pareto optimal controllers do not exceed 1 − \(\sqrt N /N\). Our results generalize to the case when disturbances from different classes may form coalitions.

Consideration was given to a dynamic model containing weakly coupled identical subsystems. The subsystem was assumed to admit a family of periodic solutions where the period is a monotonic function of one parameter. Requirements on the coupling under which the model has an asymptotic orbital stable cycle were established. The problem of stabilization of the model oscillations by a small smooth autonomous coupling control was solved using the results obtained. The system of two coupled conservative systems with one degree of freedom was considered individually.

In this paper the gradient-free modification of the mirror descent method for convex stochastic online optimization problems is proposed. The crucial assumption in the problem setting is that function realizations are observed with minor noises. The aim of this paper is to derive the convergence rate of the proposed methods and to determine a noise level which does not significantly affect the convergence rate.

We present a design paradigm for a cloud-based service for interactive modeling of traffic flows in a developing urban infrastructure. The mathematical forecasting model for the load of a transportation network is constructed as a result of synthesizing a gravitational model that describes origin-destination trips and a multimodal traffic equilibrium problem with elastic demand. The search for traffic equilibrium reduces to solving a variational inequality. Three-dimensional visualization of the transportation network and adjacent infrastructure is implemented with the virtual environment’s declarative model.

A new method was proposed to solve the global minimization problems of the Hölder functions on compact sets obeying continuous functions. The method relies on the Monte Carlo batch processing intended for constructing the sequences of values of the “quasi-global” minima and their decrements. A numerical procedure was proposed to generate a probabilistic stopping rule whose operability was corroborated by numerous tests and benchmarks with algorithmically defined functions.

We solve the problem of synchronizing a network of linear agents with unknown parameters and unknown network topology given that the Laplacian that defines it has no complex eigenvalues. To solve this problem, we use a modified high order adaptation algorithm. We obtain conditions for reaching consensus with the proposed algorithm. We show modeling results that demonstrate the efficiency of the proposed approach.

We propose an approach to organizing self-testing in a multiprocessor system under certain constraints; in particular, we use special diagnostic graphs, and the number of failures does not exceed a certain value T. We show that a test experiment where each of n processors is tested by two others lets one determine the state of all except possibly two processors for T = 4 and except one for T = 3. The total number of tests does not exceed 2n + 2.

We consider a method for finding partial solutions for the optimal motion problem of a space vehicle in a central Newtonian field on intermediate thrust arcs. This is the Lehmann-Filhés method based on knowing an incomplete integral of the Hamilton–Jacobi equations. With this method, we obtain a number of partial solutions that can be applied to solving practical problems of space flight mechanics. As an example, we solve the problem of rotating the axis of an elliptical orbit. We compare characteristic velocities necessary to rotate the axis of an elliptical orbit.

In this paper, we consider the structural modeling problem of an oligopoly market for an arbitrary number of agents, the linear and nonlinear models of market demand, and the nonlinear models of agents’ costs. The equilibrium behavior of the agents is described on the basis of conjectural variations in the Cournot or Stackelberg reaction models (in the cases of one or several leaders). The adequacy of the Cournot reaction model is demonstrated using the equilibrium modeling of the Volga region telecommunication market, where the price functions and agents’ cost functions for the voice and Internet services are defined by statistical analysis methods.

The advantages and basic concepts of model-based predictive control (MPC) are discussed. Possible MPC application in metallurgy is outlined. An example of an MPC system for billet cooling developed for a continuous casting machine is adduced.

This paper analyzes the operation of a pseudorandom sequence synchronization system in an error control system for digital communication channels with noises. It is demonstrated that the arbitrary-level error coefficient can be measured.

We address the problem of strategically supported cooperation for linear-quadratic differential games with nontransferable payoffs. As an optimality principle, we study Pareto-optimal solutions. It is assumed that players use a payoff distribution procedure guaranteeing individual rationality of a cooperative solution over the entire game horizon. We prove that under these conditions a Pareto-optimal solution can be strategically supported by an ε-Nash equilibrium. An example is considered.