Vol 55, No 3 (2016)

A nonlinear dynamic system with a random jump structure is considered. When the system’s structure changes, the plant’s nonlinear characteristic changes in a jump and the input random binary signal also changes. The structure change is registered by the structure indicator; however, its indications are error prone. A Bayesian recurrent algorithm for controlling the plant structure and probability distribution of the plant state is developed.

A two-parameter family of optimal curves in the brachistochrone problem in the case of Coulomb friction is found. The problem is represented in the form of the standard time minimization control problem. The normal component of the support reaction is used as control. It turned out that the formula for the optimal control, which does not include adjoint variables, has a singularity at the zero motion velocity. A system of ordinary differential equations is derived for which the solution of the Cauchy initial value problem makes it possible to obtain optimal trajectories that have a vertical tangent at the initial point. The self-similarity property of such trajectories is proved. It is shown how this property can be used to obtain by scaling all optimal trajectories from the set of optimal trajectories with fixed initial conditions and different terminal slope angles of the tangent.

A constructive method for the design and real-time implementation of parameterized open-loop controls in the optimal feedback control of ensembles of trajectories of incompletely determined parabolic systems with distributed parameters is proposed. This method uses reduction to semiinfinite optimization problems, alternance properties of their solutions, and additional information about fundamental laws of the application domain. The practical application of the results is illustrated by the example of controlling nonstationary temperature fields under multiple disturbances, which is a problem of independent interest.

The operational goal setting is the “first control phase” in anthropocentric objects. In terms of the Etap model, this is a change of the typical situation of the current session of the object’s operation. The structure of the operational goal setting is as follows: a priori information: (a) the given sequence of typical situations of the next anthropocentric object’s operation session, which ensures that the task of this session will be accomplished; (b) the set of typical situations describing the counteraction to external threats that can occur in the course of the execution of the session and the set of counteractions to onboard threats that frequently occur on board similar anthropocentric objects. The positive experience gained in using similar anthropocentric objects represented by knowledge matrices with the terms of the linguistic variable for each pair (typical session situation)–(typical situation of a counteraction to a threat), (typical situation of a counteraction to a threat)–(typical session situation). The precedent-based inference mechanism that makes it possible to select an appropriate typical situation and pass it to the object’s crew as the current operational goal. A classification of the threats, types of recommendations for the crew, and the crew’s dialogs with the onboard advisory operational goal setting expert system are described. This paper is a sequel to [1], and some concepts from that paper are repeated here to make it easier to understand.

A modification of the conventional bag of words model that can take into account the structural features of text documents in their classification (categorization) using machine learning techniques is studied. It is proposed to describe these features by relations on the set of certain lexemes and use the relation names, along with the lexeme names, as features. This is a distinction from the conventional model in which only unary relations are used. The effectiveness of the proposed machine learning techniques is analyzed using computer experiments on the class of the Reuters-21578 collection with eight known classifiers. It is shown that it is reasonable to apply the proposed models to classify documents using simple classifiers.

A statistical model of speed of horizontal wind in the atmosphere, intended for estimating the efficiency of stand-alone wind power systems treated as nonlinear stochastic dynamic systems, is developed. The model is based on the representation of wind as a two-dimensional Gaussian–Markov random process. The method of calculating model parameters by using observation results of the wind magnitude and direction on the land-based weather station is presented. The model parameters are calculated for several locations in Russia. More precise and simplified variants of the model are proposed. The model adequacy is analyzed by comparing the system’s efficiency indexes with their reference values.

The nonlinear dynamics of a closed automatic control system with sinusoidal pulse-width modulation is analyzed. As a result of the studies, maps of dynamic modes and bifurcation diagrams are constructed. New types of Border-collision bifurcations are discover. The concept of a design mode for systems of the considered class is introduced. The results of the work make it possible to extend the classification of Border-collision bifurcations.

In this work, the problem of a spacecraft’s rendezvous is considered in the radial coordinate system, taking into consideration the effect of the difference gravitational acceleration, using a control algorithm with the prediction model based on the minimization of the generalized work functional. The analytical formulas have been derived to compute the control actions when the motion of the center of mass and the motion about the center of mass, when solving the parametric optimization problem, are considered in a unified terminal formulation. The analytical solution is based on a special prediction model that has an analytical solution in the advanced modeling of the rendezvous process. The results of modeling a spacecraft’s rendezvous are presented.

We consider an approach to the generation of control functions in the mathematical model of aircraft motion based on the methods of dynamical inverse problems. We focus on finding control functions for the model of motion with controls in the form of an angle of attack and a thrust equivalent. We show that the algorithms ensuring the solution of the main problems of vertical navigation can be constructed. In this case, the control functions are obtained as solutions of some nonlinear equations. We present the results of simulations of the stage of an aircraft’s take-off using the algorithms developed by us.

Control of an electromechanical system consisting of two rigid bodies connected by an electric motor is considered. Both bodies can rotate about a common axis. This system is a simplified model of a precision turntable mounted on an orbital space vehicle and designed to reduce the apparent accelerations of a container with a payload fixed on the turntable. The accelerations to be reduced are small and may be comparable with the accelerations caused by the friction in the bearings of the electric drive. A feedback control law is proposed, which, after finite time interval, provides a predetermined motion of the second body relative to the first one in the presence of friction with unknown and variable parameters and in the presence of other uncontrollable perturbations. The effectiveness of the suggested control law is illustrated by numerical simulations.

This paper presents an approach and a corresponding mechanism for adjusting resource use strategies under conditions of uncertainty. Situations of competition between two economic agents are considered in which individual agents can affect the general characteristics of resources (particularly, the price). The proposed approach allows one to choose strategies depending on one’s interests regardless of the behavior of other agents as in the case of perfect competition.