Teoriâ i sistemy upravleniâ

The problem of modal control by output for a fourth-order dynamic system with two control inputs and two measured outputs is considered, provided that the controllability index is not equal to the observability index. It is shown that this problem is solvable, despite the fact that the total dimension of the input and output vectors does not exceed the dimension of the state vector. Compact analytic solutions to this problem using matrix zero-divisors and solvability conditions of one-sided linear matrix equations are proposed. Theorems are proved that implement direct (control) and dual (observation) approaches to solving the problem for cases when the controllability index is correspondingly greater and less than the observability index. Examples are given confirming the efficiency of each approach.

The flight range maximization problem for a simplified aircraft model is considered, considering the influence of the amount of fuel on the dynamics of the center of mass. It is assumed that the motion occurs in a vertical plane under the influence of homogeneous gravity forces and homogeneous resistance of the medium. In addition, there are an active thrust force and the ability to change the angle of inclination of the trajectory. These parameters are accepted as controls. An area in the space of initial variables is constructed, for which the problem of optimal synthesis is solved. It is shown that in this area the thrust can be of maximum value, zero value or singular value. The number and consequence of the trajectory arcs with the corresponding thrust have been established.

The problem of distributed control of oscillations of an effective (averaged) medium corresponding to a two-phase medium of slightly viscous liquids is considered. The averaged model is described by a boundary value problem for an integro-differential equation. It is shown that for this model, it is impossible to bring vibrations to a state of rest in a finite time by force action on the entire region.

Stationary and stable periodic modes of spatial motion of the aircraft are considered. The influence of aerodynamic asymmetry on critical flight regimes is studied using direct calculation of their parameters using continuation on a parameter technique. The reasons for the appearance of aerodynamic asymmetry under symmetric flow conditions are described. The influence of the aerodynamic asymmetry on the possibility of entry into a spin and recovery control are analyzed. The sensitivity of the spin parameters to uncertainties of the mathematical model of aerodynamics is studied using robust analysis tools.

In the framework of computational experiments a management model of the multiuser communication system is being investigated. The control scheme consists of simultaneous transmission of equal internodal flows along all shortest routes. During the experiment, the failure of each node is consistently considered while maintaining the rules of dispatching. Arrays of data are being created that reflect the system state of the damaged network. The obtained indicators are analyzed and compared with those in the original network. Guaranteed and averaged estimates of the main functional characteristics of the network during the destruction of individual nodes are constructed, taking into account the current management rules. Summary diagrams for networks with various structural features are provided.

In today's digital era, recommender systems have gained a strong foothold, becoming an important tool for effectively managing information flows. Their demand is largely due to the dynamics of current society, namely information overload and the need to personalize data. With the expansion of the scope of application of recommendation algorithms, many non-standard cases appear, for which the use of classical approaches is not so effective. This paper examines one of these: a small number of objects with a relatively large number of users in conditions of high correlation between some objects. For modeling, it is proposed to use gradient boosting, a machine learning algorithm based on an ensemble of decision trees.

In this paper, we propose a method and a specific architecture for a machine learning model that assists researchers across various fields in automatically identifying functional patterns in multivariate time series from a series of experiments. The initial problem was formalized in terms of machine learning, eliminating the need for researchers to be experts in the specific subject matter under examination. The effectiveness of the method has been demonstrated in the field of neurophysiology with data where the existence of the P300 pattern is already known. For further research, it would be beneficial to generalize the proposed method to other areas, such as sensor data from production lines or banking transactions.

Relay controls are used to solve the problem of moving an inertialess manipulator from a given starting position to a desired final equilibrium position. A method for finding relay control switching points has been proposed. The main issue is to find the conditions for a solution to a nonlinear boundary value problem of a system of differential equations that determines the trajectory of a manipulator.