Vol 58, No 4 (2019)

Nonconservative mechanical systems with one degree of freedom are considered. The goal is to provide the existence of steady-state oscillations with the prescribed properties. The system’s behavior is modeled by a second-order autonomous dynamical system with one variable parameter describing the amplifying coefficient of the control action. A numerical-analytic method to find the amplifying coefficient is proposed. Conditions of the orbital stability are obtained for the steady-state oscillations. An example of the application of the method is provided. The proposed approach can be applied to solve control problems and to find periodic solutions of second-order autonomous dynamical systems.

We propose a method for solving the control problem of a system with allowance for the dynamics of actuation mechanisms. The aim of the control and kinematic properties of the system are determined by the holonomic and nonholonomic constraints imposed on the phase coordinates of the control plant. Control actions are generated with allowance for conditions for stabilizing the constraints in the numerical solution of the equations of the dynamics of a closed system.

The article considers the problem of the optimal control of a switched system (SS) the continuous state change of which is described by differential equations and the instantaneous discrete state change (switching) by recurrence equations. The switching times and their number are not given in advance. The control quality is characterized by a functional that takes into account the costs of each switching. The problem of finding the minimum number of switchings at which the value of the quality functional does not exceed the given value is solved together with the problem of synthesizing the optimal positional control.

We propose a constructive technology for solving parametrizable problems of multichannel optimal control in systems with distributed parameters under conditions of a given accuracy of uniform approximating the resultant spatial distribution of the controlled variable to the desired state. The developed technique uses the parametrization procedure of the sought control actions and the subsequent reduction to the special form of the task of semi-infinite optimization, which is solved by the scheme of the alternance method proposed earlier; this scheme is generalized to the investigated situation. We present an example (which is of interest by itself) of time-optimization of the process of nonstationary heat conductivity with two boundary control actions.

Algorithms for fast and superfast solvers of large systems of linear algebraic equations are proposed. These algorithms are constructed based on a novel method of multistep decomposition of a multidimensional linear dynamic system. Examples of the analytical synthesis of iterative solvers for matrices of the general form and for large numerical systems of linear algebraic equations are presented. Analytical calculations show that the exact solution in iterative processes with zero initial conditions is obtained already at the second iteration step. Investigation of the synthesized solvers of large linear equations with numerical matrices and vectors the elements of which are normally distributed showed that the iterative processes converge at the third or fourth iteration step to a highly accurate solution independently of the problem size.

As data that have multiple views become widely available, the clusterization of such data based on nonnegative matrix factorization has been attracting greater attention. In the majority of studies, the statement in which all objects have images in all representations is considered. However, this is often not the case in practical problems. To resolve this issue, a novel semi-paired multiview clustering algorithm is proposed. For incomplete data, it is assumed that their views have the same indicator vector, and the paired matrix is introduced. The objects that are close to each other in each view must have identical indicators, which makes regularization and reconstruction of the manifold geometric structure possible. The proposed algorithm can work both with incomplete and complete data having multiple views. The experimental results obtained on four datasets prove its effectiveness compared to other modern algorithms.

The problem of modeling angular noise of distributed radar objects is considered. Analytical expressions determining the correlation functions of angular noise of a multipoint object and of its geometric model composed of virtual radiators are derived. Conditions under which these correlation functions are equal to each other are obtained. It is shown that the geometric models composed of virtual radiators are able to adequately replace reflections from distributed radar objects, i.e., the correlation functions and the angular noise distribution functions of the object and the model are equal.

The simplest two-criteria examples of a vector optimization problem and a zero-sum game are considered to study the adequacy of using mixed strategies if the linear convolution is replaced by the Germeier’s convolution (the inverse logical convolution) for parametrizing the set of optimal solutions or values of the game and also for estimating the payoffs of all participants. It is shown that the linear convolution yields different results in a comparison with the averaged inverse logical convolution. The issues of stochastic vector optimization and various conceptual formalizations for the value of multi-criteria mixed strategies games are discussed.

A new efficient algorithm for solving the linear separable problem of the synthesis of a communication network called the generalized method of potentials is considered and justified. It is a generalization of the known method of potentials for solving the standard transportation problem. The finiteness of the proposed algorithm is proved.

The problem of estimating the model parameters for predicting a quality indicator for an output product of a reactive distillation process is considered. The feedback loop in the prediction error of the output variable is used in the mathematical model. It is shown that this approach increases the accuracy of identifying a plant. The predictive model obtained is intended for being used as part of the improved system of the control of the technological process.

The article considers the problem of improving the coordinate-time support of GLONASS, which implies refining the models of a wide range of stochastic error components caused by inaccurate knowledge of geodetic and geodynamic parameters, such as the position and displacement rate of the geocenter, Universal Time, pole shift, irregularities of the Earth’s rotation, precession, and nutation. It is shown that the problem can be solved only using a comprehensive measurement technique that includes the use of various information measurement “techniques,” namely, global navigation satellite systems, quantum-optical communication stations, Doppler velocity sensors, and very-long-baseline radio interferometers. The problem of aligning coordinate systems on which the application of a particular information technology is based that arises from using this approach is discussed. Mathematical models, algorithms, and the results of their development in the experiments on the alignment of coordinate systems used in global navigation satellite systems and quantum-optical communication stations are given. The presented results contain estimates of the misalignment between different coordinate systems, including misalignment by center position and misalignment due to difference in the scale factor and orientation with respect to the inertial coordinate system.

The structure of the algorithm for failure detection in the duplicated sensors of a tracking system is synthesized heuristically. Using the method of mathematical simulation and search by the criterion of the maximum probability of maintaining the operational state, the parametric synthesis of the algorithm for the flight speed control system with sensor duplication is performed. The algorithm is universal for the types of failures which allow the detection of all failures that lead to the distortion of the output signals of the sensors.