Vol 77, No 9 (2016)

For a system consisting of an arbitrary number of free-running oscillators, consideration was given to the problem of speed. The system is governed by a bounded scalar control, the terminal point being defined by the desired configuration of oscillations. Solution of the problem was illustrated by examples.

We consider a general approach to constructing efficient iterative procedures with extension and localization principles, sufficient optimality conditions, and global estimates. We pay special attention to new constructive methods based on the minimax control improvement principle of V.F. Krotov. As an in-depth example, we solve the optimization problem for a therapeutic process. This is the second of two papers devoted to approximate control optimization; it continues the first one [1], which proposed a general scheme for solving the said problem and considered in detail the stage of finding the initial approximation.

Based on the backstepping method, this paper proposes a robust control algorithm for nonlinear plants under parametric uncertainty and external bounded disturbances. The algorithm ensures tracking of the plant output to a smooth reference signal with a required accuracy in the steady-state mode. In comparison with the existing analogs, control system implementation requires only one filter of dimension coinciding with the plant relative degree and observers used for calculation of the stabilizing and basic control laws. This feature considerably simplifies the control scheme and calculation of its parameters. And finally, simulation results illustrating the performance of this scheme are given.

For the model of autoregression with a random coefficient, the estimate by the least absolute deviations (LAD) method was proved to be consistent and asymptotically normal. For the asymptotic relative efficiency of the estimate by the LAD method as compared to the least squares method, an analytical expression was obtained. For the case where the innovative field of the autoregression process has the Tukey distribution, consideration was given to the behavior of the relative asymptotic efficiency.

For the distance learning systems, consideration was given to generation of individual tasks with limited performance time, and an algorithm was suggested to solve it. Such problem comes to that of integer stochastic programming with probabilistic constraints. Considered were the distributions of the random student’s time of response to the task such as the Van der Linden lognormal model and the discrete model based on empirical data. It was assumed that task complexities are estimated either by an expert or by using corresponding algorithms. For the case of continuous distribution, an algorithm was proposed based on the branch-and-bound principle. Results of the numerical experiments were presented.

After a series of publications of T.E. O’Neil et al. (e.g. in 2010), dynamic programming seems to be the most promising way to solve knapsack problems. Some techniques are known to make dynamic programming algorithms (DPA) faster. One of them is the graphical method that deals with piecewise linear Bellman functions. For some problems, it was previously shown that the graphical algorithm has a smaller running time in comparison with the classical DPA and also some other advantages. In this paper, an exact graphical algorithm (GrA) and a fully polynomial-time approximation scheme based on it are presented for an investment optimization problem having the best known running time. The algorithms are based on new Bellman functional equations and a new way of implementing the GrA.

The modern design principles of converters for multicomponent two-terminal network parameters (MTNP) are considered. The time- and frequency-domain methods are compared, and the structure of a MTNP converter is suggested. A universal algorithm of MTNP calculation based on measuring data is described.

For the nonlinear minimum phase single-input single-output (SISO) systems, this paper formalizes the structure of the equivalent “input–output” representation taking into account the smooth perturbations that do not belong to the control space. Using this representation, we design a basic combined control law ensuring the asymptotic stability of the tracking error. In contrast to the traditional approach with generation of a reference signal and a perturbation, the complex estimation of the external signals and their derivatives employs a sliding mode observer. And finally, we formalize the physical implementability conditions of the invariant tracking system in the case when only the output (controlled variable) and the reference signal are directly measured.

The paper analyzes the key trends of integrated manufacturing control based on overall process condition monitoring. The relationship between strategic goals and routine tasks executed at various supervision and control levels is discussed.

A game with restricted (incomplete) cooperation is a triple (N, v, Ω), where N represents a finite set of players, Ω ⊂ 2^N is a set of feasible coalitions such that N ∈ Ω, and v: Ω → R denotes a characteristic function. Unlike the classical TU games, the core of a game with restricted cooperation can be unbounded. Recently Grabisch and Sudhölter [9] proposed a new solution concept—the bounded core—that associates a game (N, v,Ω) with the union of all bounded faces of the core. The bounded core can be empty even if the core is nonempty. This paper gives two axiomatizations of the bounded core. The first axiomatization characterizes the bounded core for the class G^r of all games with restricted cooperation, whereas the second one for the subclass G_bc^r ⊂ G^r of the games with nonempty bounded cores.