卷 78, 编号 7 (2017)

Consideration was given to the problem of fault diagnosis of the linear dynamic systems by the nonparametric method distinguished for the fact that the system parameters may be unknown. An approach was proposed to fault localization. Methods of making decisions from the results of diagnosis were examined.

This paper presents the statement and solution to the problem of synthesis of the anisotropic control that guarantees some prescribed level of attenuation of the uncertain stochastic disturbances affecting the linear discrete time-varying system on finite time horizon. The anisotropy of a random vector is considered as a measure of the statistical uncertainty of the disturbance. The closed-loop system capabilities to attenuate the external disturbances are characterized by its anisotropic norm. The synthesis problem solution is formulated in form of sufficient conditions of existence of a controller that guarantees the anisotropic norm of the closed-loop system to be bounded by some given threshold level. The controller synthesis algorithm is based on solving the system of matrix inequalities recursively.

To provide a highly efficient control of nonlinear systems in the presence of nonmodeled dynamics and external perturbations, a new control law with feedback based on the sliding modes with an observer of the “Super-Twist” kind was proposed. For acceptable use of the continuous observer signal in the controller, presented were adaptive laws for adjustment of the control system parameters. Using the methods of Lyapunov function, system stability (convergence to a zone) was proved. This technique was proposed as an example of control and stabilization of the position of a parallel manipulator (Gough–Stewart platform). The presented mechanism with six degrees of freedom is used to control the secondary mirror of the “Large Millimeter Telescope Alfonso Serrano” situated in the state of Puebla, Mexico.

Conditions for stability and roughness of a distributed plant control system with a controller close to the degenerate system (Schipanov’s controller) were considered. The given operator relations between the plant output and controller are used for mathematical description of the plant and controller. For the linear plant, conditions were given for close-to-invariant behavior of the plant output. For the nonlinear control-linear plant, conditions for boundedness of the plant output, upper bound of the norm of the “action-output,” and the sufficient condition providing closeness of the output behavior to the invariant one were given.

We propose a method for solving quantile optimization problems with a loss function that depends on a vector of small random parameters. This method is based on using a model linearized with respect to the random vector instead of the original nonlinear loss function. We show that in first approximation, the quantile optimization problem reduces to a minimax problem where the uncertainty set is a kernel of a probability measure.

We consider a multicriterial optimization problem for volumes of buffers in a production line. We assume that the line has a series-parallel structure, and during its operation equipment stops occur due to failures, stops that are random in the moments when they arise and in their durations. The volumes of buffers are integer-valued and bounded from above. As criteria we consider the average production rate of the line, capital costs for installing buffers, and the inventory cost for intermediate products. To approximate the Pareto optimal set we use evolutionary algorithms SIBEA and SEMO. Problems with larger dimension experimentally support the advantage of the modified SEMO algorithm with respect to the hypervolume of the resulting set of points.

We study optimal approximations of sets in various metric spaces with sets of balls of equal radius. We consider an Euclidean plane, a sphere, and a plane with a special non-uniform metric. The main component in our constructions of coverings are optimal Chebyshev n-networks and their generalizations. We propose algorithms for constructing optimal coverings based on partitioning a given set into subsets and finding their Chebyshev centers in the Euclidean metric and their counterparts in non-Euclidean ones. Our results have both theoretical and practical value and can be used to solve problems arising in security, communication, and infrastructural logistics.

This paper considers the models of tolerance originating from the well-known Schelling’s publication. It is demonstrated that tolerant threshold behavior (including Schelling’s model) can be reduced to Granovetter’s model with a definite threshold distribution function. We study a model describing competition within a group simultaneously with absolute sympathy for an opposite group (a sort of “converse tolerance”). These two types of behavior are examined in continuous time, taking into account the effects of forgetting and delay that cause damped and sustained oscillating processes.

For a generalized stochastic network with a given multi-dimensional distribution of arcs duration, we propose an analytical and simulation-based procedure to calculate the probability of all critical paths, the distribution function and the first two moments of the project completion time. The procedure employs a specially constructed system of inequalities binding the task completion times.

This paper suggests a formal lattice-based method to represent the desires and intentions of an intellectual agent and to select an executor in a group of such agents while planning a new task. The method is illustrated using an example of group control for unmanned aerial vehicles.