Nº 5 (2024)

Algorithms for solving local and global boundary value problems for nonlinear and quasilinear nonstationary control systems in the class of piecewise constant controls are developed. Constructive sufficient conditions are found that guarantee the existence of solutions to these problems. In addition, a Kalmantype criterion for local and global controllability of nonlinear and quasilinear stationary systems, respectively, is obtained. The performance of the algorithms is illustrated by numerical simulation of the solution to the problem of controlling the motion of a robotic manipulator.

Discrete linear and extended Kalman filters of integer and fractional orders are presented for estimating the state and unknown parameters of linear and nonlinear discrete fractional order systems. A comparison of traditional and fractional Kalman filters is given. The features and advantages of the fractional algorithm are considered, which are illustrated with examples of using discrete linear and extended Kalman filters.

In this paper we describe in detail the iterative method of global improvement of an arbitrary given control in a nonlinear dynamical system, proposed by V. F. Krotov. Then we discuss various options for applying the Krotov method to a problem of stochastic probabilistic optimization.

The problems of optimal control of continuous systems with phase constraints are considered. It is assumed that the trajectory of the system can be divided into sections, on each of which a set of active phase constraints is fixed. Such trajectories are typical for hybrid systems in which the transition from one site to another is considered a switch. Applying the necessary optimality conditions for hybrid systems with intermediate constraints, we obtain a solution to the initial problem with phase constraints.

Previously, a method was proposed for solving the classical transport problem in an integer formulation, based on the decomposition of the original problem into a sequence of two-dimensional problems with recalculation of the coefficients of the objective functions. The method was then extended to cover additional points of production and consumption. This paper considers the case when transportation costs for additional points are proportional to arbitrary powers of the transportation volume.

The paper presents a method for preparing data for machine learning for semantic segmentation of informative classes in images based on clustering for solving problems of space monitoring of impact areas. A classification of clustering methods by various criteria is given. The choice of hierarchical clustering methods as the most effective for working with clusters of arbitrary structure and shape is substantiated. A general scheme for calculating a clustering model is given, which includes, in addition to the clustering itself, procedures for data tiling, estimating the optimal clustering parameters, registering objects, and assessing the quality of the obtained data. A scheme for preparing data for machine learning is shown, including the construction of a reference markup, calculation of a clustering model, markup correction, and testing the obtained clustering models for different informative classes on new images.

The questions related to the research of the model of functional dependence of the engines thrust on their operating parameters in the interests of reducing the asymmetry of the aircraft thrust due to the different thrust of its engines are considered. The purpose of the study is to control the rotor speeds of aircraft engines on the basis of a three-dimensional model of the dependence of engine thrust on their rotor speeds of turbine rotors of low-pressure compressors and high-pressure compressors. Methods of mathematical statistics and hardware-software modeling were used in the study. The results of the study showed and confirmed the possibility of balancing the thrust of aircraft engines when controlling the rotor speeds of its engines in flight. A three-dimensional model of engine thrust dependence on the values of rotational frequencies of its two rotors has been developed. This model allows to provide control of rotation frequencies of both rotors of the engine by means of additional fuel supply to them for formation of new values of these frequencies according to the results of comparative estimation of their values taking into account the values of their first derivatives as sign-variable special corrections providing automatic control of speed and direction of change of controlled values of frequencies.